The U.S. government made a concerted effort yesterday to convince American Jewish leaders visiting here with Vice president Mondale that the Carter administration, despite its public utterances, believes that Prime Minister Menachem Begin is in the best position among Israeli politicians to lead Israel to Middle East peace.

In the midst of this effort, the American delegation and Israeli cabinet ministers received word of President Carter's statement in Washington that if the Israeli-Egyptian initiative bogs down, the United Nations may be called upon to resume the Geneva Conference.

The statement - and particularly its timing - appeared to stun the Israelis and the American doplomats.

Israeli government sources said they were offended and they expressed fears that resumption of the Geneva peace talks would lead to inviting the Soviet Union back into the peace process.

The American diplomatic delegation expressed disappointment because release of Carter's remarks appeared to them to undermine the purpose of Mondale's visit to Israel.

In the second day of Mondale's four-day Middle East visit, which will include a trip to Cairo on Monday. Mondale and top-level diplomatic officials stressed in private meetings earlier yesterday that they are convinced not only of Begin's political strength in Israel, but of his ability to achieve at least the basis for a peace settlement.

U.S. Ambassador Samuel W. Lewis, in a private briefing for the 27 prominent American Jewish leaders who came here with the vice president, emphasized that the Carter administration regards Begin as potentially more flexible than he appears to be.

The purpose of Lewis' message, according to several American Jews who attended the meeting, appeared to be to try to undo the perception that the Carter administration regards Begin as an intransigent obstacle to peace in the Middle East.

The report of Carter's remarks to U.S. news executives came as about 500 Israeli and American officials, guests of the U.S. ambassador, gathered at the King David Hotel for a gala reception to commemmorate the 30th anniversary of Israel's independence.

The Israeli ministers and U.S. diplomatic officials, saying they had not read Carter's statement, publicly declined to comment. However, privately, some of them said they were confused that the president would make such a statement to coincide with attempts by Mondale to reestablish United States support of Begin as a leader in the peace process.

Earlier in the day Lewis and other American diplomatic officials repeatedly emphasized that they believe that Begin ultimately will become more flexible on limited territorial concessions on the occupied West Bank and Gaza Strip, and that the prime minister would set the stage for possible border changes and Palestinian Arab self-governance in the years ahead.

While the officials acknowledged that Begin's theological and historical attachment to the West Bank would make such border changes unlikely while he was in office, they told the Jewish leaders they believe that at least the prime minister is capable of paving the way for such a shift after he leaves the government.

Lewis' briefing and similar comments made by Mondale privately to members of his entourage underscored the purpose of the vice presidential trip here - an attempt to reaffirm America's special relationship" with Israel and to renew the Middle East peace efforts by extracting from Begin some private indication of flexibility that can be conveyed to Egyptian President Anwar Sadat in advance of arranging a foreign ministers conference later this month in London.

The purpose of discussions with the Jewish leaders was sharpened by published remarks by Israeli Agricultural Minister Ariel Sharon, who charged that the Carter administration was attempting to undermine Begin.

"It is impossible not to get the impression that the United States administration wishes to bring about the resignation of the prime minister," Sharon said.

The remarks by Sharon and others illustrate the extent of nervousness among top Israeli officials over the possibility that the United States will draft a peace plan of its own and impose it upon Israel with threats of withdrawing military and economic aid. During Mondale's visit, U.S. officials have sought to dissuade Israeli leaders of that notion.