President Carter, in the privacy of his mountaintop retreat at Camp David, yesterday sought to induce Egyptian President Anwar Sadat to resume peace talks with Israel and work for a compromise on the Palestinian issue.

The two leaders held their first day of talks in the snow-covered seclusion of Maryland's Catoctin Mountains, with only fragments of new reaching the world outside.

According to administration officials, President Carter is urging the frustrated Egyptian leader to seek, with American support, a compromise on breaking the impasse over Sadat's demand for "self-determination" for the Arab Palestinians.

Israeli Prime Minister Menachem Begin has said his nation can never accept that, because to Israel "self-determination" is a code-term for a Palestinian state ruled by the Palestine Liberation Organization. Begin calls that "a mortal danger to Israel."

To overcome that barrier, U.S. officials said, Carter is advocating that Egypt and Israel work from compromise language used by Carter at Aswan, on Jan. 4, which Sadat endorsed at that time.

The Aswan formula said, in part:

" . . . There must be a resolution of the Palestinian problem in all its aspects. The problem must recognize the legitimate rights of the Palestinian people and enable the Palestinians to participate in the determination fo their future."

This language, while deliberately couching the word "determination" in ambiguity, also employed two phrases that Israel opposed: "legitimate rights," and solving the Palestinian problem "in all its aspects."

Israel is concerned that these phrases imply commitments going considerably beyond its offer to provide "self-rule" to Arab Palestinians in the Israeli-occupied West Bank of the Jordan River and in the Gaza Strip, with Israel maintaining military and police rights. Nevertheless, U.S. planners believe that the Aswan formula can be the takeoff point for a compromise on this largest barrier to drawing up principles for negotiations.

Although Sadat has blamed Israeli intransigence for the Jan. 18 breakoff of Egyptian-Israeli political talks in Jerusalem, and American official said Egypt in turn cannot be "indifferent to the concerns of the Israelis."

On other issues the United States is closer to the Egyptian view. Carter, in his earlier Aswan meeting with Sadat, also said, "there must be withdrawal by Israel from territories occupied in 1967 . . ." But Carter did not say "all the territories," as the Arab nations demand, although the U.S. position calls for only minor changes in the pre-1967 borders.

Carter publicly has proposed "an interim soslution for a joint administration" to deal with the Palestinian problem. Under his approach, the West Bank and the Gaza Strip, occupied by about a million Arabs, might be administered jointly by Israel, Jordan and the Palestinians, with a "Palestinian entity or homeland" tied into a "strong federation or confederation with Jordan."

There was no indication from the presidential talks at Camp David yesterday of Sadat's reaction to any of these or other repeatedly explored issues.

"President Carter feels the discussions have gone well," it was reported in mid-afternoon by White House press secretary Jody Powell. With the press barred from the mountain retreat, Powell was the sole source of news, almost all of it physical descriptions of the scene.

Reporters had no way of knowing whether what they were told in advance actually was being discussed in the talks. However, there was no reason to doubt that Carter was attempting to allay Sadat's undisguised suspicions about what he claims are Israel's wholly inadequate responses to his peaceful overtures.

Administration officials said before the talks began that Sadat seriously fears that the Israelis are engaged in "a strategem" to prolong the negotiations, and the United States must force Israel into an agreement. U.S. officials say they are attempting to convince Sadat that this objective is beyond their capacity, and that Egypt must recognize that Israel as a democratic society has evolve its own consensus in order to compromise.

From Camp David, Powell relayed word to reporters at the White House that "both presidents feel that the relaxed and private atmosphere . . . contributed to very friendly and open discussions . . . up to a point . . .

Carter and Sadat met privately yesterday morning from 10:15 to 11:30, then walked in the clear, crisp air in a temperature of 22 degrees to a larger lodge, Laurel, where they met with advisers who arrived by helicopter from Washington.

The officials who joined them included Secretary of State Cyrus R. Vance and national security affairs adviser Zbigniew Brzezinski and their deputies, plus Egyptian Foreign Minister Mohammad Ibrahim Kamet, Sayed Marei, speaker for the Egyptian People's Assembly, and Egyptian Ambassador Ashraf Ghorbal.

Talks continued over lunch with the larger group, and Carter and Sadat met privately afterward. Interspersed during the day were brief family activities: President Carter sledding with Amy - "on Amy's sled" - Powell reported, and a post-luncheon violin duet, by Amy and her friend, Ana Gasteyer.

These touches of informality and family intimacy are not totally without a diplomatic purpose. Carter counts on employing his personal rapport with Sadat to reassure the troubled and dynamic Egyptian leader that the United States will do its utmost to support his peace initiative, while Carter seeks to dissuade Sadat from lurching into actions that disrupt the diplomatic pattern.

The talks continue at Camp David until afternoon, with further discussions on Sadat's Washington schedule until departure Wednesday.