President Carter and his chief foreign policy advisers pushed ahead yesterday with final preparations for next week's Camp David summit conference on the Middle East despite fresh Israeli concern that continued fighting in Lebanon could seriously affect the summit's prospects.

While Carter held three separate strategy sessions with his advisers at the White House, U.S. and other western diplomats were trying to reassure the Israelis that Syria was not trying to torpedo the summit with its military moves this week against Christian militia in Lebanon, according to diplomatic sources.

Israel's concern is so acute that Prime Minister Menachem Begin has been considering leaving Defense Minister Ezer Weizman at home rather than bringing him, as planned, to Camp David, it was learned in Washington yesterday.

This possibility came up during Carter's strategy sessions, which included a discussion of the Lebanese situation. But the White House is almost certain at this point that Weizman will come, according to a well-placed source.

The Israeli defense minister has met privately twice with Egyptian President Anwar Sadat and established strong personal rapport with the Arab leader.

Sadat and Begin are expected to arrive at the presidential retreat in Western Maryland Tuesday afternoon. After initial separate talks, Carter will bring the two leaders together for lunch on Wednesday, according to diplomatic sources.

Carter's approach during the lunch and over the first full day of the talks is expected to be low-key, personalized and aimed at reducing tension between the Israeli prime minister and the Egyptian president, who have traded harsh accusations in public since direct talks were broken off in July. Carter's first task will be to reestablish rapport between the two men before substance is brought up and the full negotiating delegations are brought into the meeting, according to a senior U.S. official.

Yesterday, Carter discussed the substance of his efforts to get Egyptian-Israeli negotiations resumed with Vice President Mondale, Secretary of State Cyrus R. Vance, Defense Secretary Harold Brown, Central Intelligence Agency Director Stansfield Turner, national security adviser Zbigniew Brzezinski and White House political adviser Hamilton Jordan.

White House press secretary Jody Powell told reporters later that Carter had asked Mondale "to assume responsibility for virtually all the other activities of government" during the summit. Carter will be devoting his attention "to the maximum extent possible to this conference," Powell said. Mondale will also participate in some of the shuttle to Camp David to summit discussions.

Israel began publicly linking Lebanon to the summit on Thursday, when Foreign Minister Moshe Dayan said concern over the "creeping occupation" of Christian-held territory by Syrian troops would be conveyed to the "highest levels" of the U.S. government after the Israeli delegation to the summit arrives in New York on Sunday.

The Israelis are also concerned over the visit by Syrian Foreign Minister Abdul Halim Khaddam to Moscow which concluded yesterday. Khaddam denounced the Camp David summit in a Soviet interview, calling it "a new step toward betrayal . . . of the Arab people."

The Israeli delegation will come to Camp David determined to appear flexible, and is reportedly concerned that Syria may try to provoke Israeli intervention into Lebanon during the Summit. U.S. sources report that, while the situation in Lebanon remains volatile, they see no signs of preparations for a Syrian move that would threaten the Israelis.

Meanwhile, Begin, speaking to American fund-raisers at a rally in Israel, said he would favor a mutual defense treaty with the United States if it would further the peace process. "It is in the interest of the United States to have Israel as an ally in the Middle East and Israel is a faithful ally of the free world," he said.

But he rejected the presence of U.S. troops in the West Bank and Gaza Strip to protect a Middle East accord. In his first public response to Carter's reported willingness to offer such a presence if it is needed, Begin said, "We do not want foreign soldiers to defend our people. We shall defend our people ourselves."