The Israeli Cabinet gave unanimous support yesterday to the position Prime Minister Menachem Begin took in his talks with President Carter, indicating that the Begin government does not intend to compromise with the views outlined last week at the White House.

While it is clear that Begin's mission to Washington ended in failure and that the confrontation with the Carter administration is going to cause Begin serious political trouble here, it does not seem at this time that the forces opposed to him are either strong enough or organized enough to bring down the government.

Spokesman Aryeh Naor said that the Cabinet had dismissed with contempt a highly publicized news report that an unnamed American official had called for the removal of Begin from power. The United States has vigorously denied the report.

Begin and his Cabinet met for five hours to discuss the Washington talks and, as expected, the Cabinet not only approved the positions taken by Begin and Foreign Minister Moshe Dayan, but also reaffirmed that the goal of the Begin government is to regin momentum toward a comprehensive peace plan with the Arabs, Naor said. Begin's peace proposals were also reaffirmed as a fair basis for negotiation.

After the meeting, Begin announced his intention to answer Egyptian President Anwar Sadat's most recent letter later this week to try to regain momentum in th epeace process. he said he would be making some suggestions of his own.

The Egyptian government said Saturday after a two-hour meeting of its top policy body, the National Security Council, that it intends to press on with efforts for a Middle East peace despite the fallout from the Israeli military moves against Palestinians in southern Lebanon.

In a comment on the domestic reaction to Begin's trip the Jerusalem Post said in an editorial this morning, it was "only natural" that the bad news from Washington "should have brought to the surface strong political undercurrents calling for (Begin's) replacement at the helm of the nation.

"Mr. Begin deserves the nation's wholehearted support" for resisting some of the American demands which were unacceptable, the paper said, but Begin had turned out to be his "own worst enemy" in that he had "permitted ideological considerations to impede the effectiveness of presenting Israel's case in the United States."

The crisis with the United States over policy might have come no matter who was in charge, the Jerusalem Post suggested. It added, however, his "wholly unnecessary statement on the inapplicability of United Nations Resolution 242 to the West Bank" as well as the "amateurish confusion attending the settlement s charade" had simply made matters worse and damaged Israel's position abroad.

Begin's largest coalition partner, the Democratic Movement for Change with 15 seats in the Knesset, is on record as opposing Begin's view that Resolution 242 does not require Israeli territorial concessions on the West Bank. There is talk of replacing Begin with a new political alignment, perhaps made up of elements of the Democratic movement> the opposition Labor Party and liberal elements in the ruling Likud party. Defense Minister Ezer Weizman has been mentioned as a possible replacement for Begin.

This has not advanced beyond the talk stage, however, and Weizman has had his wrists slapped for a recent newspaper interview in which he called for a "peace government," seemingly implying that the present government was not a peace government.

The prime minister is known to be angry at Weizman for this seeming attempt to undercut him. Despite Weizman's denials tha the menat to criticize his boss, all the factions that make up the Likud party have rushed into print with officials statements expressing their support for Begin. Weizman's political star may be on the rise, but his hour has not yet come if he means to hint that he might be a possible replacement for Begin at this juncture.

Nevertheless, the degree to which Begin and his supporters have used the alleged and unattributed remark of an American official, who is supposed to have called for Begin's replacement is a measure of the government's unsecurity. There ar efew things more effective in uniting Israeli public opinion that resistance to American pressure - be it real or imagined.

The Labor federation's Davar editorialized today that the real question was "not who the senior American was who said something nasty about Begin, but who the senior Israeli was who fomented this artificial minicrisis. Who wanted to generate anti-American hysteriaz" the paper asked, should deal with the Middle East crisis as "a full partner and not as a negotiator or mediator," the officials Egyptian Middle East News Agency reported.

The president was speaking to a visiting delegation from American universities.

He said that if the Palestinian question were solved "in all its dimensions, 90 per cent of the other problems will be solved and we can achieve peace in no time," the news agency said.