President Anwar Sadat and Israeli Prime Minister Menahem Begin wound up their summit today reporting "progress" toward an Israeli troop withdrawal from the Sinai and agreement on a format for continuing their quest for peace.

The Egyptian and Israeli leaders admitted, however, that they remained far apart on the most difficult question confronting them - the future of the 1.1 million Palestinians living in the Gaza Strip and on the West Bank of the Jordan River.

When they went to bed last night, Begin said today, he and Sadat still hoped to be able to issue a joint declaration of their peace intentions at the conclusion of their two-day meeting. But they were finally forced to face up to the fact that a mutually acceptable formulation on the "Palestinian problem" was not going to be found during this round of talks.

"It emerged that the differences of opinions on this matter were basic," Begin said.

Both men insisted, however, that they regarded their talks as successful and their progress toward peace as substantial. They vowed, peace as substantial. They vowed, too, to press ahead with their efforts to work out an agreement on the Palestinian question.

"For sure, we shall find a solution," Sadat told a joint news conference held at the conclusion of their talks. "I don't think there is any gap that cannot be bridged between us."

Despite the air of let down that prevailed here today among journalists who had been led by Egyptian and Israeli officials to expect a dramatic announcement at the conclusion of the talks, experienced analysts tended to agree that Sadat and Begin had achieved as much as could reasonably be expected in the short time.

"I have come here a hopeful prime minister and I am leaving a happy man, "Begin said. "The conference in Ismailia has been successful . . . Now starts the phase of the most serious negotiation: How to establish peace between Egypt and Israel as part of a comprehensive settlement throughout the Middle East."

Sadat, who has staked his reputation and perhaps his life on his daring bid to bring peace to the Middle East, was less forthcoming than usual in his replies to questions. His attention, at times, appeared to wander. But he, too, appeared to feel that an irreversible process had been set in motion.

"It is now not more than 35 or 40 days since my visit to Jerusalem," Sadat said. "Everything has changed since that visit took place. I quite agree with those who say that the world after the Jerusalem visit is completely different to the world before the visit."

Nevertheless, Egyptian editors, who saw Sadat after Begin had departed for a flight over the Pyramids and home said that Sadat appeared uncomfortable at what he regarded as a less than sufficient Israeli response to his initiative.

Asked if Begin had made concessions, Sadat said: "Mr. Begin may consider that, from his own viewpoint, he made concessions but, in my view, he has not."

Another questioner asked whether Israel had yet taken the "difficult decisions" that Sadat, during his trip to Jerusalem, said would be necessary. The Egyptian leader replied: "No, not yet."

The two sides did find points on which they agreed.

Addressing some 500 journalists in a makeshift auditorium at a Suez Canal Authority hydraulic research center, Sadat and Begin outlined these subjects on which they had made progress:

Two Cabinet-level committees, one military and one political, will be established and will begin meeting regularly next month.

The military committee, which will be chaired in turn by Egyptian War Minister Gen. Mohammed Ghani Gamassi and Isaeli Defense Minister Ezer Weizman, will meet in Cairo starting Jan. 7, officials said. Among other things, it apparently will deal with details of an Israeli withdrawal from the occupied Sinai and security arrangements between the two countries.

The political committee, headed in turn by Israeli Foreign Minister Moshe Dayan and Egyptian Foreign Minister Mohammed Ibrahim Kamel, will meet in Jerusalem starting Jan. 14. Sadat and Begin said this committee would attempt to work out differences between the two sides on the Palestinian question.

While both committees were originally expected to be made up solely of Israeli and Egyptian representatives, Sadat said he and Begin agreed the political committee would include representatives of the United States and the United Nations.

The Cairo preparatory talks, which have been meeting spasmodically since Dec. 14 to work out arrangements for a Middle East peace conference, will be upgraded to the ministerial level.

Only Egypt, Israel, the United States and United Nations have been attending these talks, however. After today's session, the preparatory conference recessed until after the new Israeli-Egyptian political and military committees have met.

While no timetable was set today for the new committees to complete their work. Begin told reporters on his arrival back in Israel that "it may be assumed that they will work for roughly between one month three months.

"We hope that they will bring us an agreement," he said. "If there is an agreement, it will serve as the foundation for the peace treaty."

Beyond the substantive announcements, a number of other declarations by the two leaders today also indicated progress that would have been beyond the imagination only two months ago.

Begin, who long insisted that return of Judea and Samaria to Arab control was simply out of the question, agreed today that Israel would have to negotiate with the "representatives of the Palestinian Arabs" over the future of the West Bank and the Gaza Strip.

Sadat, for his part, appeared to agree that the future of the Palestinians can legitmately be discussed without the participation of the Palestine Liberation Organization.

"The PLO is now in the rejection camp," he declared. I sent them an invitation (to the Cairo talks), and they refused and excluded themselves. Well, I did't exclude them," Sadat declared.

The changed that has taken place in the past six weeks is also reflected in the casual way Begin and Sadat speak about their bilateral problems.

"It is not the Sinai that is the problem now," Sadat declared today. "What concerns us . . . is a comprehensive settlement . . . Sinai, this is a side issue."

Whether the results of the Ismailia summit will be sufficient to keep up the wave of popular enthusiasm for Sadat here in Egypt remains an open question.

Within hours of the end of the talks, radical Arabs were renewing their campaign against the Egyptain leader. Syria's state radio accused Sadat of taking another step toward surrender and preparing "to conclude a seperate peace agreement with Israel at the expense of the Arab nation."

The anger was fueled by the failure of Sadat and Begin to achieve a break-through at Ismailia on the one really difficult issue - the West Bank.

It was expected from the beginning that this would be the sticking point, and it was, as the outcome of these talks showed.

Informed sources here said that the visit to Egypt last week of Israeli Defense Minister Weizman put an end to hopes for a quick resolution of this issue, because he reported back to Begin that Sadat was determined to hold out for Arab sovereignty over the West Bank.

But, Begin declared following his return to Israel today, he and Sadat worked late into last night trying to hammer out a "common text," on the Palestinian issue.

Finally, Begin said, "we decided to postpone the meeting until the morning on the assumption that we, after the night, after further thought, would find, for this issue too, a text which could be acceptable to both sides."

But, he said, the gap was too wide to bridge at this metting. So the Israelis finally proposed to Sadat that each side announce "its position with its contents in its own language." Sadat, Begin said, accepted this idea "without any hesitation, on the spot."

The two positions, as read by Sadat, were as follows:

Sadat read out as follows:

"The position of Egypt is that on the West Bank and the Gaza Strip, a Palestinian state should be established. The position of Israel is that the Palestinian Arabs in Judea and Samaria and the Gaza Strip should enjoy self rule."

To outside observers, there may not appear to be much difference between "self rule" and "Palestinian state." But in this context, the distinction is crucial because it represents the difference between Israeli and Arab sovereignty over territory that Sadat regards as inalienably Arab.

Sadat said Begin had "shown his will to end the military government on the West Bank, but we differ upon the issue of a Palestinian state in the Western Bank and Gaza through self-determination."

He and Begin said this matter would be taken up by the political committee, on which the Israeli chief delegate will be Dayan, who opposes any arrangement that would permit Arab military forces into West Bank.

Begin said he had brought to Sadat "a proposal for self rule for the first time in the history of the Palestinian Arabs, but his detailed proposals - which were not revealed - were clearly not enough.

During the press conference, Begin bantered a bit with the press. One reporter who asked a long winded, flowing question was complimented by the prime minister on his "poetry."

Sadat, normally at home with the press, seemed subdued and inclined to formula answers. But the two shook hands warmly with broad smiles at the conclusion of the press conference.