Pledging themselves once again to persevere to the end in their quest for peace in the Middle East, Presidents Carter and Anwar Sadat met tonight to discuss Carter's proposals for overcoming the few remaining obstacles to a treaty between Egypt and Israel.

Sadat, serious and subdued, and Carter, looking tired after his allnight flight, praised each other lavishly in their brief statements and stressed their determination to succeed. But neither predicted the outcome of this latest American venture into Middle East politics.

Carter was welcomed to Egypt by hundreds of thousands of people who cheered him as he rode in from the airport in an open car on a chilly, overcast afternoon. Then, for nearly 2 1/2 hours, first alone, then with their top advisers, Sadat and Carter discussed the package of compromises and diplomatic circumlocutions that Carter presented to Israeli Prime Minister Menachem Begin.

A White House statement said, "The talks focused almost entirely upon the unresolved issues and the negotiation of a treaty of peace between Egypt and Israel." In keeping with the noncommittal report, American officials declined to characterize the talks or describe the atmosphere in which they were held. and in fact there was little basis on which to judge where the negotiations stand.

Presidential press secretary Jody Powell said it was "too early to tell" and that it was "impossible to predict the outcome." Another round of talks is to be held Friday in Alexandria and Powell said it was likely that Carter and Sadat will talk informally on the train in which they are traveling from here to the port city.

Carter's two-day stay in Egypt is half state visit, complete with motorcades and sightseeing, and half negotiating session aimed at concluding the difficult and protracted negotiations that Carter has kept alive with lastminute interventions.

There also is a parallel set of discussions about Egypt's long-range strategic position in the Middle East after the fall of the shah of Iran and of Egypt's request for sophisticated American weapons. Those talks are being conducted by Secretary of Defense Harold Brown and national security adviser Zbigniew Brzezinski.

But the most pressing business is Carter's attempt to win Egyptian approval of the Carter proposals in a version close enough to the way they were submitted to ensure that they will then be adopted by the Israelis.

The Egyptian response to the Carter proposals has been favorable, leading to a surge of optimism here -- an optimism not shared by American of ficials on the flight from Washington who cautioned that serious issues remain to be settled.

It appeared today that their apprehensions might be justified when Egyptian Prime Minister Mustafa Khalil said Egypt would seek some changes in the Carter formulas. Speaking to reporters after meeting with the rest of the Cabinet to discuss the proposals, he said: "We studied them last night and we have prepared our counterproposals to the American proposals and there will be some changes."

Khalil asked for a special meeting with Secretary of State Cyrus Vance to inform him of the changes Egypt is seeking. They met for about 50 minutes before Carter talked to Sadat.

Khalil did not specify what changes Egypt is seeking in the proposals, which themselves have not been officially revealed. There is a school of thought, which includes some highranking Egyptians, that Egypt is seeking not so much specific changes on difficult issues as the appearance of driving a hard bargain, for political reasons. But there also are hints that Egypt is not yet satisfied with the proposals for settling the issue of Palestinian autonomy in the West Bank and Gaza.

This was reflected in the exchange of remarks by Sadat and Carter, who stood together on the balcony of the palace where Carter is staying addressing the press and television cameras.

Sadat, addression Carter as "one of the greatest statesmen of our time," told him: "You will find the Egyptian people firm in their dedication to a just and comprehensive peace in the area. We are determined to enable our Palestinian brothers to realize their national rights and regain their freedom."

While no conceivable formulation on Palestinian autonomy to emerge from these talks has any chance of being accepted by the Palestine Liberation Organization, Sadat wants enough, in the way of guarantees of Palestinian autonomy and Israeli withdrawal from the occupied territories, to enable him to avoid the charge of having made a separate peace.

Carter, in responding to Sadat, did not mention the Palestinian issue specifically. But he alluded to it by saying, "I have come to the Middle East to advance the cause of peace between Egypt and Israel. A treaty between these two great nations would be a begining, not an end. It would bring us much closer to the broader goal we seek -- a real peace, a comprehensive peace, a peace that would reflect the legitimate needs of all those who have suffered so deeply during the last 30 years of conflict, enmity and war."

Egypt and Israel have not yet agreed on whether the peace treaty should include a timetable for implementing the local self-government in the occupied territories that was written into the Camp David agreements. According to a variety of sources, the other unresolved issues include:

Renewed Israeli demands for guaranteed access to oil from the Sinai, a question that the Egyptians thought was already settled.

Language spelling out the relationship between this peace treaty and Egypt's defense pacts with other Arab states.

Israel's desire to have full diplomatic relations as soon as its military withdrawal from the Sinai is completed, while Egypt wants to wait until the Palestinian autonomy program is implemented.

At the airport, Carter received Egypt's grandest official greeting, complete with red carpet, 21-gun salute, guard of hohor and a band that played the "Anniversary Waltz" as Carter shook hands with Egyptian Cabinet ministers and religious leaders and American officials lined up to greet him.

The two presidents stood in an open limousine for the entire 10-mile, 50- minute ride to Kubbeh Palace, a century -old relic of the Egyptian monarchy where Carter is staying.

Cater smiled and waved to the hundreds of thousands of cheering, chanting Egyptians who waved banners and shouted greetings as the motorcade rolled by. The route was entirely through the upper middle-class suburb of Heliopolis, so Carter was spared the sights and smells of the impoverished, decrepit neighborhoods where most Cairenes live. That also meant smaller and less obstreperous crowds.

Although the Egyptians he saw were friendly, enthusiastic, even excited, they were fewer in number than those who greeted Richard M. Nixon in 1974. The motorcade also lacked the spontaneous, stirring enthusiasm of Sadat's triumphant return from Israel in 1977.

Perhaps it was because, as one spectator said, "We have been waiting now for peace for more than a year. If Carter has brought peace, we can give a better farewell." It may also have been that with only three days notice, the government did not have time to organize a big migration from the provinces.

Still, there were more than enough people making more than enough noise to fulfill the government's promise of a warm welcome. Holding children aloft, they cheered and smiled and shouted, "Welcome Carter."

Just outside the airport, a rock band in snazzy white suits serenaded the entire motorcade, even the press. On the median strip of the airport road, some Egyptians prayed as they waited, while entire families, enjoying an official holiday slready proclaimed in honor of the anniversary of the revolution in Syria, played and picnicked.

"Well Come Karter," the banners read. "We announce, approval and trust in Carter." "Welcome peace. National Cement Co."

A fleet of helicopters kept watch overhead and security forces lined the route. But aside from a few overenthusiastic spectators who rushed out into the path of the limousine, no incidents were reported.

The warm welcome prompted Carter to depart from the prepared text of his arrival statement to say, "Hundreds of thousands of Egyptians lined the streets this afternoon to express their deepest feelings -- feelings not of personal friendship for me, or even for their noble and beloved leader, President Sadat, but their deepest feeling, expressed hundreds of times over was a genuine desire for peace."