President Carter returned to the Middle East today to sound out the Saudi government before his meeting Wednesday with Egyptian President Anwar Sadat.

The President went immediately from the airport to a meeting with King Khalid, and later tonight met at the royal guest palace with Crown Prince Fahd.

En route from New Delhi, a senior administration official cautioned against expecting major developments from the talks here and predicted that Fahd would press the Saudi position of favoring "self-determination" for the Palestinians along the West Bank of the Jordan River and the Gaza Strip.

In a surprisingly optimistic comment, however, the official said of the Saudis: "It would appear they may be in the process of moving to our approach on the Palestinian issue."

The basis for that optimism - which was greeted with skepticism by some observers here - remained unclear as Carter met with the Saudi officials tonight.

The American official also told reporters aboard Air Force One that Carter, when he meets with Sadat, will seek the answer to three questions:

What does Sadat expect from the political and military talks between Israel and Egypt, expected to begin in Jerusalem and Cairo in mid-January?

What kind of positions will Sadat put forward when full peace negotiations with Israel begin?

What are Sadat's specific objections to Israeli Prime Minister Menachem Begin's proposals on a limited form of self-rule for the Palestinians on the West Bank and in Gaza?

The President, the official said, will say specifically: "How do you evaluate these things; how far are you prepared to go; what are your objections?"

The future of the Palestinians is the single most crucial and difficult issue in the peace process, which Carter is seeking to broaden and accelerate in his meetings with Arab leaders.

Saudi Arabia, Egypt and the other Arab states are demanding creation of an independent Palestinian state on the West Bank and in Gaza. Begin, in his Christmas Day meeting with Sadat, proposed something quite different: self-rule for the Palestinians that would be limited presence in the two areas and the continued existence of Jewish settlements there.

This was the context of the President's return to the Middle East today, his second swing through the region in less than a week during his trip to seven countries.

Carter's Wednesday meeting with Sadat was put together at the last minute and not announced until New Year's Eve while the American party was in Tehran, Iran. It is clearly designed to reassure Sadat of American intentions, particularly since Carter, in a television interview last week, made comments that Sadat interpreted as support for the Israeli plan.

Since that interview, U.S. officials have sought to change that impression, saying the United States has never endorsed the Begin peace plan and only considers it "a good starting point" for further negotiations.

The President's overnight stop here will soon be overshadowed by the meeting with Sadat in Aswan, and in one sense is only o prelude to it. But Saudi Arabia, although not a direct participant in the Middle East peace negotiations, remains a major influence in the Arab world. Its cooperation could be crucial in reaching a peace settlement.

Moreover, the Saudis have drawn closer to the United States in recent years and now seek additional military equipment and technology while contiuing to be the United States' major oil supplier.

Last month, at a meeting of the Organization of Petroleum Exporting Countries, the Saudis led the way in imposing what is effectively a six-month freeze on world oil prices. Today, the newspaper Arab News reported. "Saudi Arabia expects to gain political advantage [in today's talks] in return for its moderate stand on oil prices."

Tonight, following all of the meetings, American officials provided virtually no information, putting off until later answers to such questions as whether Carter had promised the Saudis the additional F-16 fighter planes they seek.

The President, arriving in Riyadh in warm, sunny mid-afternoon, was greeted by a military honor guard and by the unexpected appearance at the airport of his chief political adviser, Hamilton Jordan.

Jordan had remained behind in Washington when Carter began this journey last Thursday and his pressence here was not expected. He arrived in Riyadh on Monday, passing through Cairo and meeting with Saudi officials today.

"I just wanted to see it," Jordan said in explaining his appearance for today's and Wednesday's talks on the Middle East.

But White House press secretary Jody Powell offered a different theory for Jordan's arrival. "He probably got tired of farting around in Washington and decided to come over," Powell said.

At the airport, King Khalid offered Carter what may have been the briefest official welcome ever tendered an American president.

"Mr. President, I welcome your excellency in our country as a great friend, and I thank you for your efforts to find a just and lasting solution for the problem of the Middle East," Khalid said. "I wish your excellency a pleasant stay in this friendly country and success in your trip and commendable endeavors."

"Alsalamu Aleikum. Peace be unto you," the President replied."The primary purpose of my trip and this visit is peace."

Good-sized crowds lined Carter's motorcade route from the airport. After two days in the relaxed atmosphere of New Delhi, however, the return to the Middle East was striking. Heavily armed soldiers were everywhere, including on the floors of the Intercontinental Hotel, where the American press contingent was staying overnight.