Prime Minister Menachem Begin, under extraordinary personal and political pressure, wavered today in his intention to resign from office but promised the country he would announce a firm decision by Tuesday morning.

Leaders of the six political parties that form the government coalition, citing both political and national concerns, pleaded with him for more than two hours this morning to retract his stunning announcement yesterday that he intended to leave the office he has held since 1977.

When the meeting in Begin's office ended, various government officials spoke of "hope" and "a chance" that Begin would be persuaded to change his mind, but others expressed skepticism and said they expected a resignation. Before today's meeting, which Begin agreed to yesterday in response to the pleas of Cabinet ministers, there was virtually unanimous agreement in the Israeli press and among political analysts that the 70-year-old prime minister would go through with the resignation, probably today.

Uri Porat, Begin's chief spokesman, said the prime minister told Cabinet ministers and other officials who attended the meeting that he would consider their arguments and inform them of his decision before taking any definitive step.

"The arguments were very persuasive about the past, the present, the future," Porat said. "He finds he couldn't simply say, 'I don't want to listen to what you tell me.' Maybe that is a sign he might change his mind."

Later today, Begin was visited by other political figures from the Likud bloc coalition he leads. Israeli radio tonight quoted one of them, Ronnie Milo, as saying that Begin, who had held out the possibility of an announcement tonight, would make his intentions known Tuesday. He reportedly planned to meet with U.S. Middle East envoy Robert C. McFarlane Tuesday morning before announcing his decision.

The delay left the government and the country in a state of suspended animation, but there was also considerable public speculation on a likely successor to Begin that focused on Foreign Minister Yitzhak Shamir. Begin left his office at 1:30 p.m., and appeared to smile wanly as he entered his car. About 100 demonstrators outside the steel gate leading to the prime minister's office chanted, "Begin, the people are with you," as he was driven away.

Among the various items of government business that were frozen or thrown into doubt by the unfolding political drama was the scheduled visit here beginning Wednesday of West German Chancellor Helmut Kohl. Officially, the Foreign Ministry said the visit was still on, but there was clearly a strong chance of a cancellation if Begin resigned before then.

Egyptian minister of state for foreign affairs Butros Ghali said his government hopes that if Begin does resign, it will not have an adverse effect on the peace process in the Middle East, The Associated Press reported from Cairo.

The official Middle East News Agency quoted Ghali as saying, in the first official Egyptian comment on the announcement that Begin planned to resign: "Egypt does not prefer any one person to another (as prime minister of Israel). The important thing is a strong administration with the will and capability to carry on with the peace process."

There was still no definitive explanation for Begin's decision but little doubt that it was rooted in his apparently deteriorating physical health and his mental and emotional despondency since the death of his wife, Aliza, in November. With Israel mired in Lebanon and domestic economic problems mounting, Begin reportedly told friends he no longer felt he could discharge his duties properly.

This did not, however, prevent Begin's Cabinet and political allies from making a "truly emotional and sincere appeal" to him to stay on this morning, according to Deputy Prime Minister David Levy.

"I hope that everything that was said today about the future, about the tests facing the nation, about Judea and Samaria" the biblical names of the Israeli-occupied West Bank "will indeed have their effect," Levy said.

Levy, who is also housing minister, also figured in speculation about possible successors to Begin. But at 45, Levy is considered by many to be too young to head the government. He also lacks any foreign policy or defense experience and does not speak English, a serious handicap for any Israeli prime minister considering the country's close ties to and reliance on the United States and the American Jewish community.

The more likely compromise candidate among government ministers continued to be Shamir, 68. But whether the uncharismatic Shamir could hold together the quarrelsome government coalition, and for how long before new elections were forced on him, remained major questions.

Despite months of reclusiveness and his weakened condition, Begin's political skills and his ability to arouse public support accounted in large measure for the frantic efforts of his allies to prevent his resignation.

Asked in a radio interview why the Cabinet did "not let Begin, who is tired, resign and welcome a fresh new candidate who can carry this heavy load," Energy Minister Yitzhak Modai said:

"Because we feel that a tired Begin can carry out the missions better than any fresh young person among us."

Former defense minister Ariel Sharon did not speak to reporters when he left the meeting. The once powerful Sharon has not figured in speculation about possible successors to Begin, but he briefly demonstrated his continuing appeal to the prime minister's hard-core supporters.

Several of them gathered outside Begin's office stopped Sharon's car and embraced him when he emerged from the back seat.

The Israeli press was dominated by the unexpected turn of events, with newspaper editorials rendering various judgments on Begin's six stormy years as prime minister.

The independent Haaretz, a critic of the government, said of Begin:

"The man who left his mark on history by reaching a peace accord with Egypt, giving up all of Sinai and dismantling Jewish settlements for this purpose has, during his second term of office, become entangled in a series of failures and blunders . . . . The prime minister has done what he should have done long ago."

The afternoon independent paper Maariv, more sympathetic to the government, said Begin's current condition was a "personal tragedy for a man who never fled from any battle and never shrank from any contest," and that a resignation should not be considered "a confession of failure."