In Miami, we have a large Jewish population," the TV reporter said matter-of-factly to Nouha Alhegelan, wife of the Saudi Arabian ambassador. "What kind of support would you expect to get here?"

Alhegelan gazed back coolly. "To be a Jew does not mean you should agree with Mr. Begin on everything he's said," she replied.

This week, in an effort begun a month ago to "humanize" the war in Lebanon that has left dead, wounded and displaced throughout the country, the Arab Women's Council, which Alhegelan heads, dispatched three teams of speakers to nine American cities. It is part of an unprecedented 10-day, 20-city media blitz arranged for them by the Washington public relations firm of Gray & Co., which is headed by Robert Keith Gray, a longtime political supporter and friend of President Reagan.

Three weeks ago, Alhegelan met with Nancy Reagan and national security adviser William P. Clark about Lebanon. Then, Clark met with Saudi Arabian Ambassador Faisal Alhegelan, in a secret session that reportedly infuriated then-secretary of state Alexander M. Haig Jr. and became another factor in his decision to resign.

Although the women claim no direct responsibility for Haig's departure, many are clearly pleased that a key administration supporter of Israel is gone.

Today, after reporter Patty Oades had reviewed her intended line of questioning and warned Alhegelan that she might not find "a whole lot of support," Alhegelan said, "It doesn't matter." In English bearing a trace of an Arabic accent, she continued: "Now we're trying to tell our side. The other side has been telling theirs."

Telling the Palestinian side of the Israeli invasion of Lebanon, in fact, has become the raison d'etre for the council, which is made up of 24 wives of Arab ambassadors and about 80 other Arab-American women.

Each traveling team is accompanied by a Gray account executive to shepherd them through the rigorously scheduled appointments. Limousines take them on their rounds. Alhegelan said she and the other women are picking up their own expenses.

This campaign to take their cause directly to the American people is seen by some diplomatic observers as a radical departure for these women, whose traditional role has often been perceived as that of silent partner in their husbands' international work.

In Atlanta on Wednesday, Alhegelan and her traveling companion, Ramzieh Majali, wife of the Jordanian ambassador, met privately with Mayor Andrew Young, whose staff barred a reporter and photographer from that meeting. Then the women met with representatives of the Southern Center for International Studies and Alhegelan gave interviews to reporters from two television stations, one newspaper and one radio station.

Today, as they made their rounds in Miami, in the wake of their Atlanta blitz, the Atlanta Rabbinical Council called a press conference to give its views about the "realities of the PLO and the fighting in Lebanon."

Meanwhile, Hala Maksoud, wife of the Arab League's permanent observer to the United Nations, and Jan Barakat, wife of the Jordanian Embassy's information minister, were traveling to Indianapolis, Detroit and Minneapolis. Randa Fattal, wife of the Syrian ambassador to the United Nations, and a non-diplomat, Najat Khalil of Washington, were covering Pittsburgh, Buffalo, Cleveland and Cincinnati. All were on the same mission.

Trading stories in their hotel rooms at night, the teams reported to each other that reaction had been positive.

"I'm surprised," said Hala Maksoud. "I've never seen that objectivity by the U.S. media. And I've given talks before. We're really working at a time when I think there will be a change in American public opinion."

As part of their effort, council members staged a 12-night silent vigil outside the White House that ended July 2; launched a massive direct-mail appeal from a member's basement, and met with wives of some members of Congress who are members of foreign affairs groups.

In conjunction with the speaking tour, the council is now running controversial full-page ads in local newspapers, headlined "Begin's Holocaust in Lebanon." The ads depict a devastated Beirut street and list these figures:

* "600,000 Lebanese and Palestinians were made homeless;

* "10,000 Lebanese and Palestinians were killed;

* "30,000 Lebanese and Palestinians were wounded;

* "10,000 Lebanese were made captive;

* "And whole cities, towns and villages were levelled."

During one radio interview, Alhegelan's host noted that "the picture is quite powerful, but the statistics are debated by all sides of this war. How do we know we can believe your facts versus somebody else's?"

"You're absolutely right in asking the question," she said, listing among her sources the International Red Cross, the Quakers and Amnesty International.

Nouha Alhegelan's workday in Atlanta began at 8:30 Wednesday morning in her Omni Hotel room. Was there anything in particular she wanted to say about her mission?

"Yes," Alhegelan replied, "to tell a few facts to the American people--that it is their tax money paying for those bombs raining on Lebanon. I wonder if this is what they want to do with that money. There hasn't been yet an official investigation on cluster bombs used on Lebanon, which are forbidden by American law from anybody using them except on offensive missions."

Later, waiting for a 10 a.m. magazine interview (which eventually was canceled), the 42-year-old mother of three sons talked about misperceptions she has had to face in the three years she has been speaking to student and women's groups around the United States.

Born in Damascus to Syrian and Lebanese parents, she says she is descended from the prophet Mohammed. She was graduated from law school but married instead of going into practice. A slender woman who wears designer originals, she is considered to be one of Embassy Row's most popular and gracious hostesses.

Sitting on a low couch, she smoked a cigarette and talked about one journalist who asked her, " 'Do you have cars in Saudi Arabia?' 'Who is your president?' And by the third question I thought, 'My God, she thinks we travel only by camels and that I became a human being when I came to the United States.'

"We're all different, we're ambassadors' wives. Some have been reluctant to speak about anything, some have not been asked. Some simply didn't want to. Forget the Arab wives," she said, clasping and unclasping her graceful, red-tipped fingers and straightening her stylish culottes, "but how many ambassadors' wives in Washington do you know who give speeches?"

At 12:05, winding up a two-minute live appearance on a local noon news show, anchorwoman Lynn Harasin asked Alhegelan to explain "briefly, what do you want us to do?"

"Stop selling arms to Israel," she replied, without an instant's hesitation.

By 12:30, she and Majali were at a nearby country club, lunching with Peter C. White, president of the Southern Center for International Studies, and former Atlanta Constitution editor Harold Gulliver, now also with the center.

"I'm screaming not only for the victims in Lebanon," Alhegelan told White. "I'm screaming to prevent something much bigger. It's the whole world involved."

"I think the people in the United States are becoming aware of the danger," said White, whom Alhegelan met on a previous visit to Atlanta. "Don't you think the Jewish communities are in the same category?"

"Oh, yes, I can tell you the response," said Alhegelan. "One letter, anonymous, moved me to tears. It began 'I am a Jew and until lately, a Zionist . . .' "

At 2:30 p.m., she and Majali arrived at City Hall, where Mayor Young ushered them into his office for the "private" meeting. As Jimmy Carter's ambassador to the United Nations, Young had his own problems over the PLO when he held an unsanctioned meeting with its representatives and in the ensuing uproar resigned.

In Young's outer office, one aide explained the mayor's desire to keep the meeting private: "He has some supporters who are Jewish. We have to think of that."

Later, Alhegelan was circumspect about the visit.

"He had some good ideas--not for the Arab Women's Council--and I'm definitely going to pass them on to my husband."

At 4 p.m., WGST radio talk-show host Tom Hauck sat across from Alhegelan, taping a 20-minute interview scheduled for airing Friday. "Let's go back to 1970 when King Hussein was involved in several skirmishes with the PLO and the PLO was thrown out of Jordan," he said. "Why did that occur?"

Ramzieh Majali, a Jordanian, listened as Alhegelan replied but made no attempt to join in.

"The skirmishes between the Palestinians and Jordan is what will happen every time you have a refugee problem, where you have people in the hundreds who are wronged and living next to their home but who can't go home," said Alhegelan.

"Is the rightful homeland of the Palestinian people the West Bank?" Hauck continued.

"Well," began Alhegelan, "the rightful home for a long time has been the whole of Palestine--what is Israel today, what is the West Bank."

By 4:45, the women were en route to the Atlanta airport. In Alhegelan's lap was a folder of photographs showing scenes of the war in Lebanon.

"We have become immune to violence and war because we see it on television. It's almost impossible to convey," she said, sorting through the Associated Press and United Press International photos bought by the council for her to use in interviews.

"Do you tell someone even very close when something is really troubling you?" asks Majali, a quiet woman whose husband, Abdul Hadi Majali, was Jordanian army chief of staff from 1979 to 1981, when King Hussein named him ambassador to the U.S.

"No, I cannot, but my sister says she can tell by my eyes. It's the gaze and she says she can see my soul there," said Alhegelan.

Did King Fahd know what she was doing these days?

"I'm sure he does by now," she replied, chuckling.

"I'm almost at the limit," she continued. "It doesn't mean I'm not candid or open, but for 22 years I've been an ambassador's wife. It's a function like any other. The rules of the game are set and I play by the rules."

But does she think she's stretching it a bit now?

"Well, I don't think so," she said. "I would not be able to go beyond even if I wanted to."

She has received as much attention as she has because of her husband, she said. "That's why it has to be me and Ramzieh and Hala who are doing this. If I were just Mrs. X from Brooklyn, who would want to interview me?"

By 11 p.m., the women were settled in their Miami hotel. She and Randa Fattal, who was overnighting in Cleveland, were comparing notes by telephone. Fattal was upbeat about an unscheduled debate she had in Buffalo with a member of a Jewish women's group.

"When I said Americans should stop supplying Israel with sophisticated arms, the woman agreed," said Fattal, a Palestinian whose family has sought refuge in Lebanan since 1948. Her mother, 85, and her daughter live in Beirut--"moving constantly. They are as safe as anyone else."

Alhegelan's Miami workday began a few minutes after 9 this morning when Gray & Co.'s account executive, Peter Bray, informed her that the editor of a Miami-area weekly newspaper was moderately interested in talking with her if she could get there by noon.

"He had a golf date and he asked, incidentally, if you and Ramzieh had any bodyguards. I told him, 'Only me,' " said Bray. "He said, 'Well, if they do come, tell them to check their guns at the doors.' "

Alhegelan and Majali grimaced.

"They think any Arab's a terrorist," one of them said.

At 9:30, Patty Oades brought up terrorists again.

"The PLO hasn't a real good reputation," she said. "It's a terrorist group, yet you support it."

"Peace can only be gained if people who are denied their rights regain them," Alhegelan replied, then asked "Have you seen 'E.T.'? Even an extra-terrestrial is pleading to go home."

The talk about terrorism continued when Alhegelan told of having "qualms" about putting U.S. Marines in Lebanon.

"I know positively that the PLO and the Lebanese will not kill them, but it could be some crazy person or maybe some Israeli trying to make it look as if the PLO did it," she said. "I am scared."

But if Saudi Arabia is so anxious to see peace come to Lebanon, why has it helped to finance the PLO?

"That's a very easy criticism, it's simplistic," she said. "The PLO is the representative of the Palestinian people. The Palestinian people are in need of financial help. Saudi Arabia has the means and it will go on financing the Palestinians as long as they need it."

Standing in the 19th-floor suite overlooking Miami, Nouha Alhegelan seemed oblivious to the city stretching below her.