Menachem Begin became Israel's sixth prime minister today as his new government was formally presented to the Knesset (Parliament) and survived its first vote of confidence early this morning by a majority of 63 to 53.

It was the first time in 29 years, since the founding of the Jewish state, that an opposition party had come to power. Even among Begin's opponents, there was a sense of history and a feeling that the democratic process had been well served in a free election.

Yet the debate on the vote of confidence, which lasted more than eight hours, later degenerated into bitterness and name calling and the final vote did not come until a few minutes after midnight.

An opposition party member called a member of the coalition a liar and a bitter exchange came when the Arab mayor of Nazareth, Tewfik Zayad, a member of the Communist Party, called a Liud member a fascist and an Arab-hater. The Likud member replied in open debate "If it is an Arab like you, I really hate them."

Such bitter exchanges may not be unusual in Israel's Parliament but are generally not expressed in a ceremonial session inaugurating a new government.

In a low-key speech, notable more for its moderation than its forensic flare, Begin asked the Parliament and the nation to bear in mind the newness of the government and its policy and give it "moral credit at least for the first year of its tenure."

The new prime minister said that his government would endeavor to "deepen" the friendship of the United States, work toward a "renewal of the friendship between Israel and France" and seek the "normalization" of relations between Israel and the Soviet Union.

Begin's Likud Party, more of them dressed in coats and ties than is the custom in the Knesset where the open-neck shirt is a badge of social equality, sat in the unfamiliar seats to the left of the speaker's rostrum where the outgoing Labor Party used to sit. The gallery was packed to overflowing with friends, relatives and members of the press.

Begin, looking pale and rather like a schoolmaster, referred to President Carter's inaugural address and its quote from the prophet Micah and added his own biblical quote: "And they shall beat their swords into plowshares, and their spears into pruning hooks: National shall not lift up sword against nation, neither shall they learn war any more."

"I wish to declare that the government of Israel will not ask any nation, be it near or far, mighty or small, to recognize our right to exist," Begin said. A nation's existence was per se its right to exist, he said, and Israel's right was granted by God "at the glimmer of the dawn of human civilization nearly 4,000 years ago."

He spoke of the Jewish blood that had been spilled as the price of Israel's existence "in the land of our fathers" and said that "it is a different recognition which is required between ourselves and our neighbors: Recognition of sovereignty and of the mutual need for a life of peace and understanding. It is this mutual recognition that we look forward to. For if we shall make every possible effort."

Begin said that "all that is Hebrew within us has been bestowed upon us by the land of Israel" and that "the Jewish people have a historical, eternal and inalienable right to the land of Israel."

"Our prime concern is the prevention of a new war in the Middle East," Begin said, and he repeated his call to the Arabs to discuss with him the "establishment of true peace."

The high point of personal bitterness, anger and shouting came late in the evening when Moshe Dayan, who defected from the Labor Party to become Begin's minister for foreign affairs, came under severe criticism from his former colleagues.

Dayan said that Israel was facing a complex situation that contained both the seeds of peace and the possibility of a new war. He said the American position, as expressed recently by Vice President Walter Mondale, called for a return to 1967 borders with minor changes and a Palestinian homeland that might have a relationship with Jordan. Dayan said that Israelis and Jews around the world should be mobilized to argue against this position.

Dayan said that the new government had promised to go to renewed talks in Geneva and to honor the commitment of previous governments and that that should be enough to satisfy the new government's critics.

Opposition leader Shimon Peres of the Labor Party chided Begin for having sold out Israel's economic interest to Likud's and of upsetting the relationship between religion and state by making too many promises to the National Religious Party.

This Pere said, was done so that Begin could impose his own ideas on foreign policy, Peres said that this was the reason Begin had refused to come to terms with the comparatively dovish Democratic Movement for Change in their coalition talks.

Peres said that although his party did not agree with recent statements on the Middle East of President Carter's, the Labor Party better understood the dynamics of peace and when to make territorial compromises than did Begin and the Likud.

Yigael Yadin, the Democratic Movement leader, criticized Begin for taking his victory in last month's election as being a mandate for intransigence on territorial concessions.

The coalition Cabinet that Begin oresented is dominated by members of the Likud Party and bears Begin's personal stamp. The Likud holds nine of the 13 ministerial posts assigned so far. Another three are being held for the Democratic Movement should it wish to join the coalition later.

Dayan is far and away the most controversial appointment and the only minister who is not formally a member of the coalition. Dayan won his seat on Labor's List. He defected from Labor when Begin asked him to become foreign minister. He now sits as an independent member.

"Crossing the floor" is unusual in Israeli politics and by his defiance of tradition and convention Dayan established himself as a maverick. His appointment caused a storm of controversy when it was announced because many people in Israel still blame Dayan for the early setbacks of the October war. He was minister of defense in the Labor government from 1967-1973.

Dayan is against territorial concessions on the occupied West Bank of the Gaza Strip but his innovative mind and pragmatic approach may add flexibility to the Likud's dogmatic foreign policies.

Ezer Weizman, a former commander of the Israeli air force and the man who engineered the Likud's winning election campaign, is minister of defense. He too believes that Israel should retain the West Bank and Gaza but he believes that the Likud's frank approach to the Arabs in negotiations may succeed where previous governments have failed.

The National Religious Party, which holds 12 seats compared to the Likud's 45, is very much a junior partner but a crucial partner all the same. Its members hold interior, education, and religion posts.