The Israeli Cabinet agreed by one vote today to allow Cabinet minister Ezer Weizman to meet with senior Egyptian officials in Cairo this week, but only after a sharp political battle that appeared to deepen differences in the national unity government.

After a private meeting between Prime Minister Shimon Peres and Foreign Minister Yitzhak Shamir failed to resolve the dispute and the so-called "inner cabinet" of 10 senior ministers deadlocked 5 to 5 on the question, the full Cabinet was polled by telephone and authorized the trip by a vote of 13 to 12.

The key vote was cast by Religious Affairs Minister Yosef Burg, who had abstained yesterday when the Cabinet unexpectedly balked at approving the trip.

Weizman, a minister without portfolio who has maintained good relations with Egyptian officials since taking part in the 1978 Camp David peace conference, arrived in Cairo tonight as planned. He is to meet with President Hosni Mubarak and Prime Minister Kamal Hassan Ali.

Opposition to the journey was led by Shamir and colleagues from the right-wing Likud bloc, the main partner in the government with Peres' Labor Party.

A senior aide said Shamir would not resign as foreign minister or otherwise attempt to break up the government over the issue.

The brief but sharp political dispute was the first open, straight party-line clash between Labor and Likud and some commentators saw it as the first step toward the widely anticipated eventual collapse of the national unity government. The episode will almost certainly sour what has been described as a surprisingly smooth working relationship between Peres and Shamir since the unity government took office last September.

Nevertheless, as the telephone poll was being conducted, the two party leaders sat together smiling for photographers at the beginning of a 90-minute meeting they held with U.S. Assistant Secretary of State Richard W. Murphy.

Murphy arrived here from Amman, Jordan, on a tour of the Middle East to explore the possibility of reviving peace negotiations in the region.

Shamir surprised Peres at yesterday's Cabinet meeting by objecting to the Weizman trip. He mustered support from other Likud ministers and blocked authorization of the trip by a vote of 10 to 9.

Likud is suspicious that Peres and Weizman, in an attempt to improve Egyptian-Israeli relations, will be willing to make too many concessions to Egypt, and that they hope to encourage Mubarak's call for negotiations on the future of the West Bank and Gaza Strip.

In addition to the deep ideological differences over these issues, Shamir appears to have seized on the Weizman trip to restore his tattered credibility as the Likud leader in the government. Although the government is evenly divided between the two main parties and their allies, it has been dominated by Peres and other officials of the Labor Party.

According to an aide to Peres, when the two party leaders met this morning Shamir suggested that the Weizman trip be postponed and Peres replied that this was "unthinkable" because he had already told the Egyptians that Weizman was on his way.

"The government can't work that way," the official quoted Peres as saying.

But Shamir and other senior Likud ministers maintained their opposition during the inner cabinet meeting, forcing the poll of the full Cabinet.

Aides to Peres say that the invitation for Weizman to visit Cairo was a good-will gesture that could improve Egyptian-Israeli relations and that Weizman will not conduct any negotiations of substance during the visit.