President Carter, seeking to quash speculation that he was giving Prime Minister Menachem Begin a diplomatic cold shoulder, took time out from his political campaigning yesterday for a brief, hastily arranged meeting with the Israeli leader.

Their ceremonial get-together before a group of Democratic contributors followed a 2 1/2-hour meeting here between Begin and Secretary of State Cyrus R. Vance to discuss the progress of the Egyption-Israeli peace talks under way in Washington.

Afterward, Vance said, "There are still some problems, but we cut through some of the tough ones today."

His remark, the most optimistic to be uttered publicly by a high-ranking U.S. official in recent days, underscored the growing impression that rapid strides are being made toware agreement on an Egyptian-Israeli peace treaty.

There have been incresing private hints from various participants in the U.S.-mediated talks that, barring unexpected complications, an agreed-upon treaty will be ready for initialing within the next wek to 10 days.

However, these reports of progress have been overshadowed the past few days by speculation that the Carter administraion is irritated at Begin because of Israel's announced intention to expand its settlements on the West Bank of the Jordon River.

The settlements issue no longer appears a serious impediment to an Egyptian-Isreli peace. But the administration reportedly fears that the Israeli in other parts of the Arab world and complicate U.S. efforts to draw other Arab nations into a comprehensive Middle East peace settlement.

The speculation about Washington's pique reached its height earlier this week, when it became known that Carter and Begin both would be in New York yesterday - Carter to campaign for Democratic candidates and Begin to received an award from the New York Council of Churches - and had no plans to meet.

Administration spokesman said publicly that no snub was intended, and that the failure to schedule a meeting was due to the tight, conflicting schdules of the two leaders.

But these explanations failed to dampen the speculation about a rift, and, by yesterday, it seemed certain that the two would be forced to make a symbolic show of solidarity while in New York.

That was confirmed when Vance and Begin emerged from the prime minister's Park Avenue hotel after their meeting and announced that they were en route to see Carter.

The two then climbed into a limousine and roared up Park Avenue eight blocks to the townhouse residence of Arthur Krim, a motion picture executive and leading Democratic Party fund-raiser. Carter was there, finishing his round of New York campaign appearances with e speech to Gov. Hugh L. Carey's reelection campaign contributors.

White House press secretary Jody Powell said Carter had asked Vance early yesterday to report to him after the meeting with Begin and to ask the prime minister if he had time to come along.

There was no expectation that there would be time for substantive discussion between Carter and Begin, Powell stressed.

He added that, during the half-hour encounter on the terrace behind Krim's house, Carter simply introduced Begin to the guests. He said the president also interjected into his speech some praise for the courage shown by Begin and Egyptian President Anwar Sadat in seeking to make peace between their countries.

"We shall have soon a peace treaty between Israel and Egypt," said Begin. "I think there will be peace in the Middle East," Carter concurred.

Then the two left separately to resume their schedules. Vance, on his departure, said he was returning to Washington and would meet the leaders of the Egyption delegation later in the day to inform them of his discussions with Begin.

Neither Vance nor Begin would reveal what they talked about. Reliable sources said, though, that Vance had reviewed with the Israeli leader those treaty issues that are still unresolved and had given him the U.S. view of how they might be overcome.

The sources confirmed that Begin raised the question of U.S. financial aid the help pay the costs of Israel's withdrawal from the Sinai peninsula. There have been reports that Israel wants as much as $4.5 billion from the United States.

Until now, Washington has been non-committal about this issue, and U.S. sources have said the administration is unwilling to discuss specifec figures until the treaty negotiations seem assured of success. However, the sources were unable to specify what Vance said about the aid question in yesterday's meeting.

Since Begin's arrival here Wednesday, the sources added, the chief Israeli negotiators. Foreign Minister Moshe Dayan and Defense Minister Ezer Weizman, have briefed him on those issues where Egypt has made concessions and those where further give by Egypt seems unlikely.

Begin, who will be visiting Los Angeles and Canada during the coming week, reportedly will review the negotiators' recommendations and refer them back to the Israeli cabinet for discussion.