After a dramatic two-day delay, Prime Minister Menachem Begin said today that his decision to resign is final but he agreed to postpone the formal step that will implement it to allow his political colleagues to settle on a successor.

Begin, who was quoted as saying, "I cannot continue," made known what was described as his final, irrevocable decision to the Israeli Cabinet and other political leaders during a meeting in his office that lasted more than two hours. But at the request of the Cabinet, Begin delayed, at least for a day, the submission of his letter of resignation to President Chaim Herzog as required by Israeli law.

Tonight, Cabinet ministers from Begin's political party, Herut, met for three hours in an unsuccessful attempt to designate a successor who could hold together the six-party government coalition. The most likely candidate was thought to be Foreign Minister Yitzhak Shamir, who, according to some sources, had already reached an understanding with his principal party rival, Deputy Prime Minister David Levy.

Levy, however, said in a radio interview, "I understand there will be more than one candidate" to succeed Begin, and Transport Minister Chaim Corfu said Levy made it clear at the Herut meeting that he would run for the leadership. The prime minister did not express a preference on his successor in the meeting.

According to officials who attended today's meeting, Begin was reluctant to put off the submission of his resignation letter to Herzog and it was not clear how long he would delay it.

Before his resignation became final, Begin made one more decision regarding the problem that has hung over his last year as prime minister--the Israeli Army's continued presence in Lebanon.

At the request of U.S. special Middle East envoy Robert C. McFarlane, who reportedly conveyed a personal message from President Reagan, Begin agreed to a second postponement in the Army's planned withdrawal in Lebanon to a new line along the Awwali River north of Sidon.

The United States has been pressing Israel to delay the partial pullback for as long as possible while efforts are made to reach an agreement between warring Lebanese Christian and Druze militias that would allow the Lebanese Army to take over positions to be evacuated by the Israelis. The pullback, initially planned for last weekend but postponed because of a similar request, was believed set to start tonight or early Wednesday morning.

This second delay is expected to be for only a matter of days at most. The Israelis have said they intend to be in their new positions along the Awwali by the time of the Jewish New Year next week.

Begin's resignation decision climaxed 48 hours of high political drama that began Sunday with his surprise announcement to the Cabinet that after six years as prime minister he intended to step down. That set off a frenzied effort by his political allies to persuade him to change his mind that continued to the last possible moment today.

According to an official who attended today's meeting, Begin told his colleagues, "I cannot continue." When Begin's long-time friend and political ally, Economics Minister Yaakov Meridor, said he would not accept the resignation, the official said the 70-year-old prime minister replied that he would stand by his decision and said to Meridor in a low voice, "Yaakov, it won't help you."

Begin, who is in apparently failing health and has been despondent since the death of his wife in November, clearly convinced the Cabinet and other officials that he would not change his mind. "He's resigned. Yes, it's definite," Shlomo Lorincz, a member of the orthodox Agudat Israel party, told reporters after the meeting.

Begin has dominated Israeli politics since he was first elected prime minister in 1977 and his decision to resign is expected to set off intense maneuvering that could easily lead to early parliamentary elections in Israel, which are not scheduled until 1985.

The maneuvering effectively began with Begin's agreement not to submit his resignation to Herzog immediately. This was designed not only to allow his own political party time to agree on a successor, but also to prevent Herzog, a member of the opposition Labor Party, from asking Labor Party leader Shimon Peres to try to form a new government.

Under Israeli law, Begin's resignation will mean the automatic resignation of his government, which was formed after the 1981 elections. Herzog is then required to consult with leaders of Israel's parliament, the Knesset, and to ask one party leader to form a government.

The hope of Begin's political allies is that shortly after the prime minister officially resigns they will be able to present Herzog with a solid parliamentary majority lined up behind a chosen successor, leaving the president no choice.

Given the current makeup of the Knesset, the chances of Peres being able to patch together a new government coalition are considered remote. As of tonight, the Labor Party had made no official statement on Begin's resignation and reportedly was waiting for the actual letter of resignation to be tendered.

The choice of a designated successor to Begin by the Herut Party will not necessarily lead to the quick formation of a new government. Herut, which along with Israel's Liberal Party forms the ruling Likud bloc, would still have to win the agreement of the four smaller parties that make up the coalition government. Without those coalition partners, the Likud is far short of a parliamentary majority.

In the meantime, Begin will remain in office as the head of a "transition government." Under Israeli law, such a government, although its moral authority is weakened, has enhanced government power because no Cabinet minister can resign and votes of no-confidence in it cannot be introduced in the Knesset.

There is virtually no prospect that Begin would agree to form a new government.

His spokesman, Uri Porat, said it is "very likely" that the prime minister will retire from public life altogether, although he may maintain some involvement in political party affairs.

Even before Porat made today's official resignation announcement, reporters waiting outside Begin's office learned of it from news reports from Bonn. The reports said that West German Chancellor Helmut Kohl had cancelled his planned visit here beginning Wednesday after being informed that Begin was resigning.

As Begin left his office this afternoon, reporters scrambled to question other officials about the meeting and the process of succession.

A small crowd of supporters waved and cheered as his car whisked past them. The frail prime minister, sitting in the back seat, did not wave back.