Saudi Arabia's King Fahd arrives this afternoon to test the willingness of a newly reelected President Reagan to become more deeply involved in a drive for peace in the troubled Middle East.

Fahd, in preparation for the Washington visit, held a 2 1/2-hour meeting in his royal palace a week ago today with Palestine Liberation Organization Chairman Yasser Arafat and sent senior emissaries to Syria, Jordan and other key Arab states.

Fahd's premier position as the first state visitor of Reagan's second term, and the first of a number of Middle East leaders coming to Washington in the next several months, reflects the continuing importance accorded here to the world petroleum giant.

So does a letter delivered to Fahd Dec. 6 by Secretary of Defense Caspar W. Weinberger containing what U.S. officials described as "a very strong pledge of support for Saudi Arabian security." The Saudis interpreted the document, which has not been released, and other statements by Weinberger as a promise that the United States will sell them about 40 more F15 jet fighters.

In view of the tumultuous 1978 and 1981 battles in Congress over Saudi warplane purchases and new warnings last month from Capitol Hill, the administration announced Jan. 30 that all Mideast arms sales are being held in abeyance pending a comprehensive study of security needs in the area. The interagency study began last week and is expected to last several months, but reporters were given strong hints in a White House briefing that further Saudi arms sales are in prospect when the research is completed.

Fahd, the key figure in his country's "American connection," arrives as an extraordinary era of Saudi primacy in U.S. relations with the Arab world is ending, according to American experts. But the sources said the oil kingdom continues to be important and again could become of crucial importance if the global energy situation, or Mideast military or political circumstances, take a sudden turn.

Saudi Arabia was the No. 1 U.S. source of imported oil in 1976-81, but its U.S. sales have dropped sharply since. Saudi Arabia has now slipped to sixth place, behind Mexico, Canada, Venezuela, the United Kingdom and Indonesia because of a major program of U.S. energy diversification and the effects of the current worldwide oil glut.

Moreover, the close U.S. ties with Egypt following the Camp David accords and renewed U.S. diplomatic relations with Iraq this year make the Saudis somewhat less important than they were a few years ago as a U.S. conduit to the Arab world.

"Saudi Arabia is returning to its conventional role of not being the key Arab partner of the United States," said William B. Quandt of Brookings Institution, a former National Security Council official under President Jimmy Carter and author of a book on "Saudi Arabia in the 1980's." Quandt added that although Saudi Arabia is no longer the unchallenged No. 1 in the U.S. connection with the Arabs, "it remains among the two or three most important Arab states with which we have close relations."

A State Department official, who asked anonymity, said that Cairo, Damascus and Baghdad have been the three main poles of the Arab world for centuries and that, despite a period of intense Saudi importance since 1973, they will continue to be the most vital.

At the same time, the official said, "Saudi Arabia remains of sustained importance" to the United States and the world economy. He said it is the ninth largest U.S. trading partner, the largest holder of U.S. Treasury securities and an important factor in the politics of the Arab world.

The central question on Fahd's agenda, U.S. and Saudi sources said, is a Reagan role in reviving the stalled Arab-Israeli peace process.

The Saudis and other Arab states took satisfaction from many elements of Reagan's Sept. 1, 1982, Mideast peace plan, which came eight days before the Arab League's "Fez declaration" based on a Fahd initiative.

The Saudis are unhappy, though, that movement toward a broad Mideast settlement virtually has collapsed because of the war in Lebanon, the reluctance of Jordan's King Hussein to become involved as a negotiator with Israel and opposition to the Reagan plan by the previous Israeli government of Prime Minister Menachem Begin.

A senior State Department official, speaking at a White House briefing Friday, said the Saudis believe this is "a historic moment" following a massive new political mandate for Reagan for revival of the peace process under U.S. auspices.

The new Israeli unity government of Prime Minister Shimon Peres has "displayed more flexibility" than the Begin government about the peace process, the official said.

The possible "next step," he added, could be a successful conclusion of the recently renewed dialogue between Jordan's Hussein and the PLO's Arafat about negotiations with Israel.

Egyptian Foreign Minister Esmat Abdel Meguid, following discussions with U.S. officials, told the Associated Press yesterday he sees signs that Hussein in preparing to take the "calculated risk" of negotiations with Israel. Meguid said Egypt is urging "a more active U.S. role."

The White House briefer told reporters Friday that the United States is willing to assume a more active role only in "direct negotiations" between Israel and the Arabs.

Other U.S. sources said any decision about new U.S. initiatives is unlikely before spring or summer, after further developments in the Hussein-Arafat discussions and trips to Washington by Egyptian President Hosni Mubarak and others.

The several months' respite from major U.S. diplomatic activity and from renewed Saudi arms sales fits into a Reagan administration strategy of avoiding congressional controversy about the Middle East while the lawmakers concentrate on Reagan's embattled budget proposals.

The Saudis do not appear upset by the prospective timetable for the next round of warplane sales. The Saudis never were interested in concluding the F15 sales during Fahd's visit, according to informed sources, and had agreed from the beginning that a deal would not be submitted to Congress before April.

The Carter administration's sale of 60 F15s to Saudi Arabia, strongly opposed by Israel, was approved by the Senate, 54 to 44, on May 15, 1978. The Reagan administration's sale of five airborne warning and control system (AWACS) planes touched off a similar legislative struggle and was approved by the Senate, 52 to 48, on Oct. 28, 1981.

Both Carter and Reagan had to lobby intensively -- and personally -- to win the Saudi arms sales battles.

Other subjects on Fahd's agenda, according to Friday's White House briefer, include U.S. policy on oil prices and Saudi access to the U.S. market for its emerging $35 billion petrochemical industry, which is owned half by foreign firms, mostly from the United States.

Many different birth dates for the Saudi monarch have been reported, but his embassy said he was born in 1923, which would make him about 62. He assumed the throne on June 13, 1982, following the death of King Khalid. Fahd long has been considered the top government administrator.

Fahd is expected to place primary importance on his face-to-face discussions with Reagan, scheduled to begin at the White House Monday.

The last visit here by a reigning Saudi king was the 1971 call of King Faisal on President Richard M. Nixon. Fahd came to Washington on an official visit as crown prince in May 1977 as the Carter administration was formulating its Middle East policies.

Fahd met Reagan at the October 1981 Cancun, Mexico, summit of North-South nations, but U.S. officials said there was little more than a handshake.

Fahd is to be accompanied by Foreign Minister Saud Faisal, son of the late King Faisal; Petroleum Minister Ahmed Zaki Yamani; Finance Minister Mohammed Aba Khail; Minister of Municipal and Rural Affairs Ibrahim Angari, and other officials. Also in the party is Fahd's youngest son, Abdul Aziz, 11, who is expected to spend the week sightseeing