French President Francois Mitterrand called today for an Israeli-Palestinian dialogue of peace and said that "at the right moment" the Palestinians should be entitled to exercise their rights to achieve an independent state.

Diverging sharply from Israeli Prime Minister Menachem Begin, who expressed his strong disagreement as the two leaders addressed Israel's parliament, Mitterrand said that while Israel has a right to exist, the same right must be extended to its neighbors.

Later, Begin was forced to leave a state dinner given by Mitterrand, after he fell ill. But doctors said that the prime minister, who has a history of heart ailments, was only suffering from fatigue, Israeli state television reported.

Mitterrand called on the Palestine Liberation Organization--which he said speaks for the Arabs of the West Bank and Gaza Strip--to recognize Israel and enter into a peace dialogue.

"This dialogue supposes that each party can go to the very limits of their rights, which for the Palestinians, like others, can at the right moment mean a state," Mitterrand said.

Begin, however, asserted that with an independent state, the Palestinians would seek Israel's destruction in order to adhere to the tenets of the PLO charter, which he termed "the Arab edition of 'Mein Kampf,' " a reference to Adolf Hitler's manifesto for nationalist socialism.

While praising what he called France's historic sense of justice, and particularly Mitterrand's personal empathy toward the Jewish state, Begin said there are still obstacles to overcome in erasing Franco-Israeli animosity and establishing a full friendship between the two countries.

"The main obstacle is France's support for the concept of a Palestinian state," he said.

Mitterrand's call for a Palestinian state under the terms he outlined was not a surprising departure from his previously stated positions any more than was Begin's response, but the exchange between the two leaders before a packed chamber of the Knesset, Israel's parliament, underscored the differences that remain between France and Israel despite the atmosphere of rapprochement surrounding the first state visit here of a French head of state since Israel was founded 33 years ago.

In his speech, delivered in French, Mitterrand recalled France's record of support of the Jewish people even in the days before statehood.

But, Mitterrand said, the vital issues of the Arab-Israeli conflict cannot be resolved "by proxy," and France cannot be cast in the role of a mediator or "substitute for the real partners in a dialogue."

"What I want to make clear here today is my affirmation of the right to live. That right is yours, ladies and gentlemen, but also of your neighbors, and I include specifically the Palestinians of the Gaza Strip and the West Bank, as well as the people of Lebanon," the French president declared.

Mitterrand said he still supports the Camp David peace process--because "those who make war have a right to make peace." But he said he rejected the global approach to peace implicit in the European peace initiative drafted in the Venice Declaration of 1980 "because I prefer a peace that is achieved gradually to a peace that is never achieved at all."

"But I also believe and wish for a homeland for the Palestinians because you cannot deprive a people of its identity," Mitterrand said.

He added, "the PLO, which speaks for the Palestinians, could come to the negotiating table if only it recognizes Israel's right to exist. We know that nothing will be decided except by the negotiators themselves . . . ."

In his speech to parliament, which was interrupted several times by heckling from the floor by two members of the communist Democratic Front for Peace and Equality, Begin challenged Mitterrand to work for a nonaggression pact that would include all the countries of the Mediterranean Basin, including Israel and Arab states.

"Mr. President, please assume the initiative. Approach all the peoples who dwell in the region that is the cradle of human civilization and propose to them, with any amendments you deem fit, this Mediterranean charter," Begin said.

In a joint press conference tonight, which for the most part left aside their differences on substantive Middle East issues, Begin and Mitterrand defended their positions on Israel's proposal for limited autonomy for the 1.3 million Palestinians of the West Bank and Gaza Strip.

Mitterrand said Begin had discussed at length the autonomy scheme and had handed him a lengthy document outlining Israel's views, but he added, "I do not share the views on the question of whether this is really the solution."

The French president said he "recognizes the passion that underlies his Begin's remarks about Israel's position toward Palestinian self-determination," but that after two meetings with the Israeli prime minister, "the divergence of opinions remains."

Earlier in the day, Begin and Mitterrand met during a 2 1/2-hour working luncheon, which Israeli officials said was dominated by a discussion of Lebanon.

Begin, according to the Israeli sources, warned Mitterrand that the chances of the cease-fire along the northern border were diminishing each day as Palestinian guerrillas continue to build up their forces, but he stressed that Israel would not attack the PLO in Lebanon unless it is first attacked.

In the meantime, his foreign minister, Claude Cheysson, met with five prominent West Bank Arab leaders in the French Consulate and discussed West Bank issues.

The Arab officials, who included the mayors of Nablus, Ramallah, Gaza and Bethlehem, presented Cheysson with a memorandum that attacked "one of the most ugly occupations in history," and called for Israeli negotiations with the PLO.