A senior Egyptian official said today that Egypt would not resume politically important talks with Israel about the fate of a disputed stretch of border on the Red Sea unless the Israeli Cabinet agrees to arbitration on the matter.

"They have not yet made up their minds whether they will go to arbitration," said Abdel Halim Badawi, who has served as Egypt's chief negotiator in the talks on the disputed strip of land at Taba.

"If they say they will not go to arbitration we will say, 'Okay, we're not going to play the game.' "

Badawi's remarks in the semiofficial press this morning and a telephone interview this afternoon suggested mounting frustration among Egyptian officials at Israeli Prime Minister Shimon Peres' apparent inability to bring his Cabinet into line on the issue.

The Taba controversy, although it concerns only a few hundred yards of Red Sea beach front, has become a central symbol of the "cold peace" that has marked relations between the two countries since 1982.

Israel, after capturing the Sinai Peninsula in 1967, returned it to Egypt amid much controversy in 1982 as part of the peace signed three years before.

But when Israel invaded Lebanon only a few weeks later, the action caused an immediate and lasting strain in relations as an embarrassed Egypt was accused by the Arab world of making peace on one front, allowing Israel to go to war on another.

Last month, however, as the latest round of Taba talks was under way, Egyptian President Hosni Mubarak suggested that the border dispute was all that stood in the way of his meeting with Peres and Egypt's returning an ambassador to Tel Aviv after withdrawing him in 1982.

The central issue in the talks is, on its face, a technical one. Egypt is not demanding the return of Taba as a condition for better relations.

It maintains that its claims on the disputed land are clear and previously were acknowledged by Israel in the disengagement that followed the Suez war of 1956.

It is asking only that the issue be settled by the arbitration of a third party.

Peres and his Labor-led coalition are believed to be amenable to this process, but Israeli Foreign Minister Yitzhak Shamir and the Likud bloc that makes up half of the Israeli national unity government are opposed.

Instead, they insist on a lengthy process of "conciliation" excluding third parties. Either approach is permitted by the 1979 Egyptian-Israeli peace treaty.

Egyptian officials in the past have interpreted Likud's position as an effort to stall until it takes control of the government later this year under the national unity agreement, at which point the Egyptians are concerned that Likud will introduce new and possibly unacceptable conditions.

On Dec. 31, Peres told the Foreign Affairs and Defense Committee of the Israeli Knesset, or parliament, that Egypt was willing to carry out several commitments affecting relations between the two countries as soon as Israel agrees to arbitration over Taba, and before the arbitration actually begins.

These commitments included not only the several accords reached at Camp David in 1978, but arrangements related to locating the bodies of Israeli soldiers still missing in the Sinai; joint Israeli-Egyptian-American efforts to located the Israeli submarine Daqar lost off the Egyptian coast in 1969, and consideration of navigation procedures and landing facilities on the eastern shore of the Sinai.

Outlining in some detail the compromise formula he expected, Peres said, "the terms of reference for the arbitration will contain Egyptian agreement to try to solve the Taba dispute by conciliation during the first two phases of the arbitration process in which each side presents its case."

"Egypt will not use the precise term conciliation but instead will refer to 'solutions by other means,' " Peres said.

But Badawi, soon to take up a new assignment as Egypt's ambassador to the United Nations, said this afternoon that he had no knowledge of such an arrangement.

"We will not go to conciliation," Badawi said. "We've said that, and they know that."