In separate Independence Day television addresses to the nation, Prime Minister Menachem Begin and President Yitzhak Navon appealed to Israelis tonight to show more tolerance toward one another despite the bitter political and religious divisions in the country.

Begin--in a speech in which he also reiterated his basic foreign policies, including a rejection of any freeze on Jewish settlements in the occupied West Bank--referred to the "terrible phenomena" of domestic violence that included the death from a hand-grenade explosion of a peace activist outside his office in February.

"Let us respect one another, and each his adversary," Begin said. "Let all violence in any form be eliminated and disappear from among us. Yes, there were serious, even terrible phenomena among us. But a new leaf can always be turned whether in private or public life. Let us turn our backs on the negative phenomena of the past."

Today was Memorial Day in Israel, a day of mourning and remembrance for the nation's war dead. The contrasting, joyful Independence Day, marking the 35th anniversary of the creation of Israel in 1948, began officially at sundown and will continue through Monday.

In his speech, Begin defended Israel's invasion of Lebanon in June as a "justified defensive war" aimed only at destroying the Palestine Liberation Organization's "center of anti-Israeli terror" in southern Lebanon. He said Israel has no territorial ambitions in Lebanon but would insist on its "full right" to adequate security in southern Lebanon before withdrawing its Army.

Begin acknowledged the deterioration in Israel's relations with Egypt, which he said came about "through no fault of ours," and called for a resumption of the Camp David autonomy negotiations on the West Bank and Gaza Strip.

"The resumption of negotiations does not have to--and cannot--be conditional on the freezing of Jewish settlements in Judea, Samaria the biblical names for the West Bank and the Gaza district," he said. "This settlement is legal and derives from our inalienable right to the land of Israel."

Navon, delivering his last Independence Day message before leaving the presidency next month, was more blunt in warning against domestic intolerance and violence, particularly the growing rift between the country's observant, orthodox Jews and its secular majority.

"The question is not if there will be arguments among us but if we will know how to conduct them," Navon said. "This question has become a central factor in our lives, in our ability to sustain democracy and, quite simply, to live with each other."

The religious divisions Navon warned against were exemplified by a recent incident in which a secular Jew was critically injured by stones thrown at him when he inadvertently drove his car into an ultraorthodox Jerusalem neighborhood on the sabbath.

Appealing for a beginning effort to break down some of the barriers that separate the country's religious schools from the state schools where a majority of Israelis are educated, Navon said, "Matters are growing increasingly worse and must not be allowed to go on in this direction without our active intervention and attempt to divert them to a desirable course . . . . Unless people of good will in both camps learn to talk with each other, I sadly foresee increasingly grave developments."

Navon was much more optimistic about healing the ethnic divisions in Israel between Oriental or Sephardic Jews and the country's generally more affluent, better educated Ashkenazim community of Jews of European or North American origin. He predicted that the tensions between the two groups, which he said "have been exaggerated for political reasons," will gradually diminish and all but disappear, and he urged Israelis to "condemn those who for personal or political reasons incite and sharpen the differences."

Navon is a member of the opposition Labor Alignment and is often mentioned as a potential challenger to Begin in the country's next elections, scheduled for 1985. Many in the Labor party believe that Navon, a Sephardic Jew, could blunt Begin's appeal to the Sephardic community, the base of Begin's support.