President Carter began a new round of separate talks with Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin yesterday at the Camp David summit, in an evident effort to build on the joint conversations the three leaders have already had.

Shifting the format of the talks from the five hours of trilateral discussions they had on Thursday, Carter met alone for 90 minutes with Begin yesterday afternoon and then saw Sadat alone for 45 minutes.

U.S. officials continued to refuse to give any details of what the tree leaders are discussing at the highly secretive summit, which is now expected to end next Tuesday or Wednesday.

But informed sources said the three leaders were in excellent spirits at the end of their talks Thursday, and White House press spokesman Jody Powell for the first time characterized the atmosphere by telling reporters that "the personal relationships among all three of the principals are good" despite the long hours they are putting into negotiations.

Powell cautioned against attaching significance to the pace and form of meetings, but the variation in format yesterday clearly suggested to diplomatic observers the beginning of an intensive American effort to get each side to seek compromise by altering its initial detailed positions, which were thought to be the center of the three-way talks held Wednesday and Thursday.

The pattern of the summit began Tuesday night and Wednesday morning, when the president met alone with first Begin and then Sadat to establish their initial bargaining positions.

The president then brought the two Middle East leaders together for almost seven hours of negotiations during Wednesday and Thursday. It was reliably reported that both sides compromised on several issues but left other key points unresolved and the outcome of the summit still very much in doubt.

In resuming his separate talks with Sadat and Begin, Carter clearly was mounting his own effort to break the deadlock on those unresolved issues before bringing the two together again.

While the key sticking points and the substance of the talks remained shrouded in secrecy, American officials continued to appear carefully optimistic, suggesting that the almost dormant, Middle East peace process that begin with Sadat's visit to Jerusalem last November is "back on track" at least while the summit continues.

Briefing reporters at the American Legion hall here six miles east of Camp David, Powell said "the delegations, the principals, are involved in serious discussions of the problems that they face."

Powell described Carter as "participating actively" in the discussions, suggesting that the president has already offered a variety of American ideas for settling the many complex issues in the Middle East dispute.

Key among these are Israeli withdrawal from occupied Arab territory, recognition of Israel as a legitimate state and guarantees of its security, and a solution to the Palestinian problem.

Thursday night, following a Marine Corps dress parade on the Camp David grounds and a reception, the president, Vice President Mondale, Secretary of State Cyrus R. Vance, Defense Secretary Harold Brown and national security adviser Zbigniew Brzezinski met for almost 2 1/2 hours with Sadat and his two top advisers.The meeting lasted until 1 a.m. yesterday. Earlier Thursday, the American officials had held a similar session with Begin and his chief Israeli advisers.

Yesterday morning the same group of Americans, who were joined by White House political adviser Hamilton Jordan, held their regular weekly foreign policy meeting here. Jordan is expected to remain at Camp David through the weekend.

The presence of all of Carter's key foreign policy and defense advisers was another indication of the importance of the bilateral talks with Sadat and Begin on which the summit is now focused.