In a last-ditch attempt to save the Egyptian-Israeli talks from collapse, President Carter yesterday gave Israeli Prime Minister Menachem Begin some new proposals that appeared to keep a faint pulse of life beating in the U.S.-mediated Middle East peace process.

Although Begin's four days of talks with Carter ended in a thick air of gloom about the prospects for breaking the deadlock in the negotiations, the lasts U.S. move at last added to the suspense surrounding the effort to work out a peace treaty between Israel and Egypt.

Israeli government sources, while refusing to describe the new proposals, said they were important and different from those Carter had been urging on Begin. These sources added that Begin. These sources added that Begin had promised to realy them to the Israeli cabinet for its opinion and hoped to have reply before his scheduled departure from the United States twoard midweek.

Following Begin's departure from the White House yesterday afternoon, Carter talked by telephone with Egyptian President Anwar Sadat. The Sequence of events seemed to indicate that the U.S. president may be making one final, all-out bid to get Begin and Sadat together at a new Camp David summit meeting.

Begin came to Washington on Thursday for private talks with Carter after Israel rejected a U.S. proposal for a modified summit. Israel spurned the idea because Sadat had planned to send a deputy rather than attend himself and because Begin felt the United States was tiltng toward the Egyptian side in the negotiating disputes.

Over the course of their discussons, Begin is known to have made clear that Israel will not make any further concessions on the two major issues under dispute. These involve Israel's refusal to tie the peace treaty to separate negotiations on autonomy for the Palestinian inhabitants of Israeli-occupied territory and Israeli insistence that the treaty take primacy over Egypt's military assistance pacts with other Arab states.

Until yesterday, the United States had been advocating that Israel give ground on both points. In fact, the gap was so wide that Israeli government sources reported from Jerusalem early yesterday that the discussions here were being broken off.

Instead, there was one final session between Carter and Begin yesterday afternoon. It was then, according to U.S. sources that Carter put forward a new package of what a joint U.S.-Israeli statement characterized as "suggestions designed to help resolve some of the outstanding differences..."

The sources, while declining to be specific, said Carter's proposals dealt specifically with the major disputes. These sources denied rumors, which began circulating late yesterday after congressional leaders were briefed by Carter, that the United States might have offered to establish a military base in Israel or give Israel some kind of guarantee against possible Arab aggression.

The sources added that, in addition to Carter's brief telephone conversation with Sadat, the Egyptian leader was being sent a longer message and detailed U.S. assessment of the situation through the American embassy in Cairo. Although Begin plans to be in Washington through today and then in New York for approximately two days, there are no plans at present for him to meet further with Carter, the sources said.

Israeli sources said that, despite the contacts with Sadat, it had been agreed that Egypt will not be informed of the substance of the new U.S. proposals until after the Israeli cabinet decides whether it considers them worth pursuing. That cabinet action, the sources said, could come today.

Begin was described by these sources as "not neutral" but having a definite opinion about the new proposals. His attitudes will be conveyed to the cabinet in Jerusalem, the sources said, allthough they declined to comment on whether he is for or against following up on the new American ideas.

The general thrust of what the sources said hinted that the United States may be backing away from the concessions it had been urging on Israel and instead may ask Sadat to show more flexibility in his negotiating stance.

If so, the big question is how Sadat, who until now has shown as much adamancy as Begin will respond. Sen. Charles Percy (R-Ill.), one of congressional leaders who met with Carter late yesterday, said it was his "impression" that the president's phone conversation with Sadat didn't sould "encouraging."

But administration sources refused to agree or disagree with Percy, saying only that the next steps still have not been determined. They acknowledged only that Carter feels "deep concern" over the potential failure to achieve the peace treaty agreed to by Begin and Sadat under his mediation at the Camp David summit last September.

The disputes, which caused negotiation of the actural treaty to bog down in stalemate, stem from Sadat's anxiety about exposing himself to charges of making a separate peace with Israel at the expense of larger Arab interests.

To that end, he his insisted that the treaty be linked to a timetable for completing the separate talks, also agreed to at Camp David, on establishing Palestinian autonomy in the Israeli-occupied West Bank and Gaza Strip. Isreal, citing the Camp David accord about treating the two issues separately, has refused to accept such linkage.

Similarly, Sadat has objected to an article in the draft treaty text stating that the peace pact takes precedence over all of Egypt's other treaty obligations. To cover that point, the United States had suggested a clarification noting the right of all nations under the United Nations charter to engage in legitimate, collective self-defense.

However, Begin persistently has countered that to accept the Egyptian demands would turn the treaty into a "sham" agreement that Egypt could abrogate at will. Begin arrived in Washington Thursday vowing he would not be pressured into signing "a sham document," and he has stuck to that position throughout his discussions with Carter.

In an interview yesterday morning on "Issues and Answers" (ABC, WJLA,) Begin restated his objection.He said, "I do not belong to those who cynically say a peace treaty is a piece of paper."

The prime minister also rejected Sadat's linkage demand on the grounds that it would make Jordan, Syria and the Palestinian inhabitants of the occupied territories -- all of whom have shunned the peace process -- parties to an agreement between Israel and Egypt.

In thatcase, he asserted, the peace treaty would be "hanging on a thread" that could be broken by Egypt if any of these other parties obstructed negotiation of the autonomy issue in time to meet the target date.

The Begin said he did not believe that failure to resolve the impasse now would mean the end of the drive to create peace between Egypt and Israel after three decades of hostility. If the differences can't be bridged now, he added, "the next step should be very serious reflection, and we need some time for all the parties involved."

"I do not adopt the theory of now or never," he said. "We shall have to negotiate again, and I don't see any tragedy in it."

Carter, though, seemed much less optimistic about getting the talks moving again if the current deadlock isn't broken. The president, who has enormous personal prestige at stake in the outcome, began his day yesterday by teaching a Bible class at Washington's First Baptist Church. He told his students: "I stayed up real late last night with Prime Minister Begin. We did not make any progress."