Prime Minister Menachem Begin returned home yesterday from his tough confrontation with President Carter, and defended his refusal to bow to demands of "the mighty United States and our great friend and ally" for Israeli withdrawal from the West Bank and Gaza.

Conceding on his arrival at Ben Gurion Airport that it might have been easier to give in to U.S. pressure, Begin told reporters: "The representatives of Israel, the foreign minister and I and our advisers, felt deeply, that we are dealing with matters concerning the future of the nation and the lives of our children."

Begin also made it clear that he intends to try to rally the Israeli people behind him in his confrontation with Washington. Speaking warmly of his meetings with the American Jewish community, he said U.S. Jews were "standing together with staunch heart" behind Israel.

Begin said he had reached agreement with Carter on some issues, although he declined to identify these for the time being. But he made no secret of the fact that there had been bitter disagreements as well.

In every conversation with Carter, Begin said, there had been an important difference.

For the United States, he said, "the problems on the agenda are of policy, important policy. For us, they are problems of life and existence, and of making sure of our future."

When asked about the widely distributed comment of an unnamed American official who was reported here to have said that Begin should step down as head of government, Begin replied with some anger. "The prime minister of Israel is elected by the people of Israel, not by any diplomatic representative of the American administration."

Washington has denied that any senior official ever made such a comment.

The suggestion has Begin appearing in the Israeli press that if the comment was not fabricated in the first place, it is certainly being used by Begin and his supporters for all it is worth to rally the people if Israel behind him.

From Begin's point of view, the remark would appear almost too good to be true. Such heavy-handed U.S. pressure could save Begin from the domestic political trouble, he seems certain to face in the days ahead.

Meanwhile, Defense Minister Ezer Weizman, in an interview with Maariv published yesterday called for creation of a government of national unity - a peace government that would include members of the opposition Labor Party - to represent Israel in what Weizman called the toughest confrontation the Jewish state has ever faced with the United States.

"We must show President Carter a united people and a united government," he told the newspaper. "We must gather and recruit the best minds, just as we recruit the most praise-worthy commanders on the eve of a going war."

Asked what Weizman's remarks, Begin said he had not read the text. But, Begin said, "There is a peace government in Israel - exactly the government in which the defense minister is the defense minister."

And, Begin added, if Weizman were calling for a government of national unity that included all political parties, the prime minister said he had favored such a government all along - even when he was in opposition.

Weizman was quick to tell inquiring reporters that of course the peace government should be headed by Menachem Begin, but there are rumblings among the body politic in Israel yesterday suggesting that Weizman - along with some of the liberals in the Likud coalition, members of the Democratic Movement for Change, and some of the opposition Labor Party leaders - should break away and try to form a new government.

Leading politicians within the ruling coalition were quick to deny that such maneuvering was taking place, and it is doubtful that such a plot could succeed - even if mounted - at this stage.

The leader of the opposition Labor Party, Shimon Peres, quickly rejected the idea of participation in a government of national unity.

In his interview with Maariv, Weizman also admitted that the Israeli occupation of southern Lebanon had gone beyond the original plan.

"The original plan, political and military, was to occupy a smaller territory than what was actually occupied," he told the newspaper. "There was no advance decision on precisely how many kilometers, but certainly the intention was not for the scale that developed as a result of the requirements of the situation.

"The dimensions of the operation changed in two senses: the terrorists' resistance and their attempts to harm our soldiers continued, and the mukhtar [leaders] of the villages asked the Israeli defense force to take them under its protection.

"And there was a third factor," Weizman said. "From the moment a clear tendency emerged to send U.N. forces into southern Lebanon, we thought that advancing to the Litani River would help the U.N. to spread its forces as required and would improve the chances . . . of carrying out its task of preventing the terrorists from returning to southern Lebanon."

Although Weizman talked about an Israeli withdrawal from southern Lebanon, he warned: "If the U.N. does not carry out its task, the Israeli defense force will go back to resume its task."