THE DINNER WAS SMALL and private and held earlier this year. It was not the kind of evening that makes social news, but one that could affect Middle East politics for years to come. Outside the imposing brick house security men stood guard while inside the mood was friendly, the conversation forthright. There were about a dozen guests, many of them prominent Jews or pro-Israeli leaders. Their host, an influential Arab, was the ambassador from Baghdad, Nizar Hamdoon.

The evening was in honor of Rep. Stephen Solarz (D-N.Y.), and around the dining room with blue and white carpet, blue and white Louis XV- style chairs, and blue and white swagged draperies were Peter Rodman, chairman of the policy planning council for the State Department; Howard Teicher, director of Near East and South Asian affairs for the National Security Council; Robert Pelletreau, deputy assistant secretary of defense for Near Eastern and South Asian affairs; Alfred H. Moses, lawyer and former liaison to the Jewish community for the Carter administration; Ken Wollack, co-editor of the Middle East Policy Survey; Don Oberdorfer of The Washington Post; David Ignatius of The Wall Street Journal; and Judith Kipper, Middle East specialist at the American Enterprise Institute.

"It was an amazing evening, very interesting discussions, everyone very relaxed," said one guest. "Here's Steve Solarz, a Jewish congressman from New York, with pro-Israelis around him, talking with an Arab from Iraq."

"It was rather gutsy of the ambassador to have a group like that, some of them who were anything but friendly to Iraq," said another guest.

The dinner was typical of the groups Hamdoon puts together a mix of Jews, Christians, Moslems, congressmen, journalists and businessmen, "the kind of thing," said Robert McC. Adams, secretary of the Smithsonian Institution and a specialist on Iraq, "that one likes to imagine goes on in Washington and one doesn't often find going on."

UNTIL TWO YEARS AGO, Hamdoon's dinner party would have been impossible. Until last year there hadn't been an Iraqi ambassador in Washington and there hadn't been an Amerka3>ican ambassador in Baghdad since 1966. Iraq, led the last six years by President Saddam Hussein, was viewed by many in the United States as an outlaw nation: brutal, radical, an ally of extremist Arab leaders, an enemy of Israel, an aggressor toward its neighbors, a sponsor of Palestinian terrorist groups and a Soviet weapons client.

Baghdad, in turn, saw the United States as Israel's protector; as responsible for the lack of a Palestinian homeland, for the defeat of the Arabs in the 1967 war with Israel, for the separate peace with Egypt, for the settlements on the West Bank, for the invasion of Lebanon and for the tilt toward Iran in its war with Iraq. "The vitriolic (Iraqi) propaganda that poured out against the U.S. for 17 years was the worst in the Middle East," said James A. Placke, former deputy assistant secretary for Near Eastern and South Asian affairs at the State Department.

But by 1983 Iraq was in a fight for survival against Iran, and the regime in Baghdad wanted Washington to pressure U.S. allies from selling arms to Tehran. After having a long line of do- nothing diplomats here, Hussein handpicked a high-level official to send to Washington.

Nizar Hamdoon arrived in November two years ago with a mandate to warm the icy U.S.- Iraqi relationship. He was to turn a foe into a customer for Iraq's vast supply of oil, to persuade Americans to sell agricultural and high- technology goods on long-term credit and to sway the country's highest leaders away from their strong support of Israel.

"In 1980 the Iraqis were out in the garage," said Christine Helms, an Iraq specialist at Brookings Institution. "The word Iraq was anathema. If you worked on Iraq, or said anything nice about Iraq, it labeled you a nut case. But the same people who said this now have come around 180 degrees."

Washington seemed to view Iran as a strategic nation that might once again become an ally if Ayatollah Khomeini were deposed.

By the time Hamdoon arrived in Washington, fear of Islamic fundamentalism was sweeping the Middle East and the West. Hamdoon capitalized on the uneasiness. "He had this map, and he was going around town giving it out," Moses said. "It was supposedly taken from an Iranian soldier. It showed Iranian forces advancing through Iraq, through Jordan and Israel -- and the target was Jerusalem."

THE POLITICAL WORKINGS of Iraq are mostly a mystery. The country is ruled by the Baath party, born in conspiracy, bred in ruthless. It is a surreptitious system that excludes most Iraqis and conceals information from its own members. Its structure is based on cells, secret groups unknown to each other, with undisclosed informers. It is socialist and anticommunist; it favors uniting all Arab nations and eliminating the state of Israel. Its leader, the 48-year-old Hussein, came to power in 1979 through a series of bloody plots within his own party.

Hamdoon is a member of the Baath party's elite, called the National Command. He is clinically analytical, intellectually curious, quick to adapt and eager to reach out to his most formidable opponents. At 41, he is short and trim, with round dark eyes, a shock of black curly hair and a mustache that curls down. The son of an Iraqi army general, he is an eager student of the United States. In less than two years, he has sliced through the world of influence in Washington.

At first, he was awkward, poorly dressed, his English barely understandable. "When he first arrived he was clearly a very friendly but somewhat ill-at-ease young Iraqi who was certainly not conversant in the finer parts of diplomacy," said Geoffrey Kemp, who at the time was senior director of Near East and South Asian affairs for the National Security Council. "But with extreme alacrity he has become one of the most polished diplomats in Middle East affairs in Washington."

"It was a challenge," said Hamdoon. "Not just for me as a person, but even for the government. It isn't easy for an Iraq representative to work here after 17 years of not just having no relations, but having a very bad image."

Not only the image but the reality changed quickly. Hamdoon's once choppy, sharply accented English is now smooth enough to carry him through network TV interviews. He is frustrated that his English was better 20 years ago when he attended an American Jesuit high school in Baghdad. He said he speaks Englis "quite enough to communicate but it's not enough sometimes to be precise or eloquent." His earlier wardrobe of glaring white suits, dark shirts and white ties has been replaced with navy or gray double- breasted suits, silk ties and pocket squares, most bought in France. More astutely, he has learned whom to talk to and when.

At first he tried to approach officials in the Reagan administration. They told him, he said, they were behind him but he needed to "work on some Democrats" to get their support. He approached Odeh Aburdene, head of the Arab Bank Limited in New York, Kipper at AEI and Helms at Brookings to help him make friends in Congress, the media and academia. Influential voices were invited to small quiet meetings, to lunch at Maison Blanche, to intimate but serious dinner parties.

"The way I perceive things here in Washington, you don't need to be a diplomat," Hamdoon said, chain-smoking Marlboros in his spacious wood-paneled office off Massachusetts Avenue. The room is richly decorated: plush beige chairs sit on deeply colored oriental rugs; a crystal chandelier hangs above."I think it is better to be yourself. It is better to get out of diplomatic maneuvers. It is better to be direct and open . . . Whenever they think that you are maneuvering, you usually lose. That's the problem with many of the Arab policies here in Washington . . . They are saying something here and something else back home."

His manner is relaxed and unflappable. "On the positive side you could say he is cool," said a State Department official. "On the negative side you could see it as calculating." He is always prompt, but when an interview runs longer than scheduled, he shows no impatience.

He works late into the night and on weekends. Occasionally he enjoys watching a science fiction film. He watches television programs such as "Cagney & Lacey." He likes to see policemen on TV "control the cities where there are troubles and to control the gangs."

He almost never laughs, and when he does it is not at jokes: "Some parts of life make me laugh: the ironies, some people who feel they can control everything." He rarely smiles.

"When I see him smiling, I say, 'God, look, he is smiling,' the Iraqi press counselor.

He is straightforward. "He has always given me direct if not satisfactory answers," said Michael Neiditch, director of adult Jewish education for B'nai B'rith. "He's never given me puppy dog answers, no gobbledygook." Even his opponents find him charming. "Although we have a number of disagreements, I have always found him personable and intelligent, and I emphasize very personable," said Shireen Hunter, deputy director of the Middle East Project at Georgetown University's Center for Strategic and International Studies.

He has an agile, probing mind. "I felt pragmatism," Aburdene said. "I felt that he was like a sponge. He absorbs and listens."

His parties are not ostentatious. Guests sip his favorite scotch, Johnny Walker Black Label, and wine; waiters serve rack of lamb and hummus. The menu may not be very different from many Middle Eastern embassy dinner parties, but the guests and the conversation are worlds apart.

Joyce Starr, director of the Near East program at the Center for Strategic and International Studies, said, "I was invited to a small dinner in honor of (Iraqi Foreign Minister Tariq) Aziz. I was really surprised . . . Hamdoon directed the dinner and the questions. You go to a dinner, and it's usually blah, blah. He turned this into substance. If you were mentally tired when you arrived, you were really tired when you left."

He has tried to pull back the veil of Iraq, encouraging policymakers and business leaders to visit the country. "There's not the semblance of an open society," said one who went. The Baghdad government often pays for at least half the cost of the trip.

"I guess by now everybody in Washington has been to Iraq," Hunter said.

AT A DINNER in honor of an Iraqi archeologist, several leading museum directors are gathered in the secluded home of Samira McAllee, an American born in Iraq. The large house is filled with antique furnish- ings, ancient artifacts and contemporary paintings by Morris Louis, Helen Frankenthaler and Jules Olitski. It is an atmosphere that Hamdoon enjoys; he studied architecture at the University of Baghdad.

Before coming to Washington, Hamdoon was responsible for Iraqi cultural activities, including archeology.

"Among the archeologists and artists he is very popular," says Behnam Abu Soof, the guest of honor. He recalls two days they spent together in Mosul when the temperature was 122 degrees and they were visiting sites of ancient palaces. Hamdoon brushed aside any desire to drink water or eat food until late in the afternoon. Soof, an archeologist used to heat, says, "I couldn't stand it . . . I was afraid he would have sunstroke . . . I admired his resistance."

While guests at the party cluster in groups, Sahar Hamdoon sits silently. Her English is weak, and she is afraid to use it. She is 29, and wears a black dress and black beret with rhinestone jewelry. Her cheeks are heavily rouged and her eyes are darkened with kohl. She met Nizar when she was still in high school and he came to visit her family in Mosul. They are first cousins.

"I was sitting in the basement studying," she says later, partly in broken English, partly with the help of a friend who is translating. "My mother told me to come up and say hello, but I was wearing a robe, and I told her no. She insisted, so I came up for a few minutes." The next day Hamdoon returned for lunch, and her mother prepared a special meal of rice and meat in a lemon sauce. "He stayed an hour or two and then he left."

A week later Hamdoon called Sahar's father and asked permission to marry her. A year later, after she finished high school, they were married. This past year she gave birth to a daughter, Ula. Hamdoon says he would like his daughter to be an architect. One journalist who has spent time with him says "the fact that he is willing to talk about his daughter at all signifies to me that he's an unusual person, because in the Arab world you talk about your sons."

Sahar says her husband seldom speaks to her, that he rarely shows emotion. "When his father died last year, you could look at his face and see he was in pain. He looked sad and very tired, but he didn't talk about it, he didn't cry."

"He never talks with me about his work," she says. "When he's home, he's working. He's working in the library till 1, 2, 3 in the morning and on Saturday and Sunday. He's the same way here as in Iraq."

SAMIR VINCENT, an American businessman who grew up in Iraq and who now makes frequent trips there, said Hamdoon's role in Iraq's ministry of information was unclear. "I think that's a nomenclature used for anything. You have carte blanche . . . He comes from a position of authority. He's not just any ambassador."

Earlier Hamdoon had been the director of the party bureau in charge of Syrian affairs. There had been several plots by Syrians to overthrow the Iraqi Baath party, including an assassination attempt on Hussein. In response, 33 Baathists were executed as a lesson to others who might have had the same idea. "This is a party that . . . used to shoot itself, its own people, all the time," said Tom McNaugher, a Middle East specialist at Brookings.

Hamdoon recalls his party activities as a youth when the government was run by the military with the support of communists: "You got beaten. You could be imprisoned. You could even be executed." There were underground meetings in his college years when he headed the Iraqi federation for students. Even after the Baath party came to power, there were constant assassination plots, attempted coups and internal power struggles.

Hamdoon has portrayed Iraq as a moderate country, matured by the experience of war. The image is far from the picture many in the State Department knew when Iraq was the leader of the Rejectionist Front, often aligned with Syria, Libya and South Yemen. It was an "extremely disruptive force in the region" said a State Department official. It was a refuge for terrorists, including Palestinian extremist groups, and a hiding place for the notorious Abu Nidal, who specialized in blowing up airplanes. "Not a very nice man," said Placke.

Recently Palestinian terrorist Mohammed Abbas, alleged mastermind of the hijacking of the Italian cruise ship Achille Lauro, was traveling with an Iraqi diplomatic passport. If Abbas, now under extradition charges by the Italians, has been hiding in Iraq, "he is welcome there," Hamdoon said.

For years Iraq has made threats toward neighbors such as Saudi Arabia and Kuwait. After Anwar Sadat's trip to Jerusalem and the Camp David Accords in 1979, Iraq summoned its allies to the Baghdad Summit and expelled Egypt from the Arab League. Outright war came when Iraq turned toward Iran, and the results have been costly.

"Their reserves have been reduced from $30 billion to $1 billion, and their external debt has risen to $55 billion," said Riad Ajami, an economics professor at the Wharton School of economics and author of a congressional report on Iraqi technology. Oil revenues dropped from 2 million barrels a day in the 1970s to 650 barrels a day at the beginning of the war and are now at 1.6 million barrels a day, Hamdoon said. With new pipelines through Saudi Arabia and strengthened pipelines through Turkey, Iraq hopes to export 3.2 million barrels a day by 1987. "We'd like to sell our oil to the United States," Hamdoon said. "It's a good market for us."

When seemingly endless waves of Iranian soldiers flooded across Iraq's borders during the war, Hussein's troops apparently began using chemical weapons. The Iraqis have denied using such weapons. Hamdoon said the charges are an excuse by Khomeini for a lack of victory.

"There's no question about its (chemical) use," said a State Department official. "We are convinced through the basis of Iranians who had apparently been gassed and sent to Europe for treatment." In April last year, Newsweek magazine reported that traces of Tabun, a lethal nerve gas, had been found on the battlefield by a team of United Nations investigators.

With the Iraqis purchasing arms from the Soviets, the United States did not protest its allies supplying weapons to Iran. But with help from Hamdoon, that position has been changed. "We seem every once in a while to proclaim some state system in a region as a dominant one," Ajami said. "We proclaimed the Iraqis." The French started selling weapons to Baghdad, and other U.S. allies stopped supplying arms to Tehran.

Although goods continue to flow and some restaurants and nightclubs in Baghdad stay open almost 24 hours a day, the war has exhausted the Iraqis. "We can never relax," Hamdoon said. "We never know when there will be an attack from the north, an attack from the south."

RESUMPTION of full diplomatic relations was an Iraqi decision, but the United States made demands on Iraq. During a meeting with Solarz in 1982, Hussein said that Israel has legitimate security concerns that should be taken into account in any settlement between the Israelis and the Palestinians. At about the same time, Iraq expelled terrorist Abu Nidal.

Some Iraq observers wonder whether the changes are simply temporary in the face of war with Iran.

"We have evolved," Hamdoon said. "There are some radicals in the Arab world who we consider extremist . . . But always you see Iraq, you see Jordan, you see Egypt, you see Saudi Arabia and even Israel. If you take it in terms of decades, you can see some change . . . it's not because of the war."

As for Iraq's position toward Israel: "We have yet to see anything positive on the Arab-Israeli peace initiative," Shireen Hunter said. "They only have said that they are not going to stand in the way. Well, it's very easy not to stand in the way. The question is, are you going to help?"

"The experience we got from the '70s is that whenever the Arabs try . . . to interfere, they damage it and they did lots of damage," Hamdoon said. "So it's better to leave it to fewer countries who are directly involved with one of the borders with Israel. That means Syria, Jordan, Egypt and the Palestinians . . . It's up to them to decide. We support them as our brothers, so we don't go into details with them."

Hamdoon supports the idea of terrorist attacks in Israel "inside the occupied territories on the West Bank" and on "military targets . . . I don't agree in targeting civilians." He shook his head when asked about Israel's right to exist: "We are not going to say that until we see our Palestinian people secure and they have their self- determination rights established . . . It is a qualified no."

"One should never forget, marvelous as he is as an ambassador, that the Iraqis are armed by the Soviets and strongly anti-Israel," Ignatius said.

The United States, after an extensive period of virtually no trade with Iraq, is now doing business with that country. In the last three years, Iraq has bought $1.5 billion worth -- on credit -- of American agricultural and commercial products. The total for this year alone will be three quarters of a billion dollars. Hamdoon says Iraq wants to buy high-technology equipment for petroleum-based industries, agricultural industries, communications development and health care.

The biblical land of Mesopotamia and Babylon, where the Tigris and Euphrates rivers flowed, where civilized man was born and three major religions were fathered by Abraham, entices the fantasies of American businessmen. "I call Iraq the sleeping giant," Aburdene said. "Their oil reserves are second to Saudi Arabia. Their agriculture is strong . . . their population is hard working."

Hunter doubts the promise will be fulfilled. "Now many businessmen are seeing a downturn in the Gulf. They are hoping that Iraq is the new El Dorado . . . I don't think Iraq is going to be another Saudi Arabia either economically or politically."

The French, who have sold weapons to Iraq, "are going to want to collect," she said. "Part of collecting is to sell them stuff. It is not El Dorado. They are not going to fill American pockets."

Meanwhile, the Iraqis sink deeper in the quicksand of war. Taha Yassin Ramadhan, deputy prime minister and the second most powerful man in Iraq, told Joyce Starr of the Center for Strategic and International Studies that he had devised two economic plans,e based on the war ending in two years, the other based on its being endless, "like the Hundred Years' War."

"We are in a better economic situation than the last five years," Hamdoon said. "When you are wealthy, you look for stability. You cannot earn money, you cannot build your country and still seek terrorism and turbulence . . . Iraq would like to see itself playing a better role and a larger role for the sake of stability in the area. But with this war going on, it would be difficult."

"In Iraq," businessman Samir Vincent said, "they don't say 'Inshallah' (if God wills it). They say 'akeed' -- it will be done . . . For better or for worse, they are men of their word."