In an apparent attempt to generate public support for Israel's efforts to resist U.S. pressure to sign a peace treaty, Foreign Minister Moshe Dayan was widely quoted tonight by government officials as saying President Carter had issued a 10-day ultimatum for a settlement with Egypt.

The report was promptly denied by both the White House and Dayan, but as of late tonight, Israeli Radio continued to broadcast it and Foreign Ministry officials who had earlier confirmed the account of the ultimatum continued to stand by it.

The purpose of the story seemed to be to counteract what is widely perceived here as pressure being applied on Begin by President Carter.

Earlier today, Begin sharply disputed Carter's statement Tuesday night that "absolutely insignificant differences are now creating unsurmountable obstacles" to peace.

"I do not agree with the statement of President Carter," Begin said. "With all due respect, in my opinion these are great issues relating to the future and security of the two countries."

In Alexandria, Egypt, however, Egyptian Prime Minister Mustapha Khalil said, "I agree completely with what President Carter said."

Begin said he will go to Washington tomorrow for "personal" talks with Carter, but in keeping with the Israeli Cabinet's decision yesterday not to take part in a summit meeting now, he said that even if Khalil shows up in Washington, he will not meet with him.

The report that Carter had issued an ultimatum to Dayan was carried by state-controlled Radio Israel today.

The radio reported that Dayan told members of Israel's Parliament that prepared to devote only 10 days more to the Egyptian-Israeli peace talks, and then he will completely revise his Middle East policy.

Carter was also said to have intimated to Dayan that the United States' new Middle East policy would include a readiness to intervene militarily "anywhere" in the Middle East if necessary to offset guarantees lost in a breakdown of the Camp David negotiations.

Dayan's statement, purportedly made today in an off-the-recond briefing to the parliament's Foreign Affairs and Defense Committee, was "confirmed" by two normally reliable Israel government sources. Later, the Israeli government press office telephoned foreign correspondents at their homes and reiterated the Israeli radio report, without elaborating on the substance of it.

Neverthekess, Dayan flatly denied tonight that he told the committee that Carter had said anything about devoting only 10 days to the peace talks, or that Carter told him he was considering a new Middle East policy.

The White House also issued a strong denial of the Israel Radio report. White House press secretary Jody Powell told reporters that President Carter said the remarks attributed to Dayan were inaccurate, adding: "We certainly have set no deadline in this matter."

Earlier in the day, Begin said that "great issues" remain unresolved in the Middle East peace talks, and that if the United States attempts to exert pressure on Israel to give ground, he will "reject" the pressure.

While Begin did not specify the outstanding issues, government sources said that some of the most serious obstacles include new Cairo proposals that would re-establish Egypt's presence in the Gaza Strip making it, in effect, an Egyptian vassal state.

Egypt, according to the Israeli sources, is insisting on its own police garrison and liaison office in Gaza, and that Israel transfer administrative authority to Egyptian officers rather than to the Palestinians living there.

According to the Israeli view, the Egyptians, who lost control of the Gaza Strip to Istael in the 1967 war after occupying it since 1948, have abandoned the original Camp David intent to establish autonomy for Gaza Strip Palestinians.

Begin said his refusal to meet with Khalil while he is in Washington this week is not based on any dislike or affront because of their differing political statures but because such a meeting would "not only not be useful to the peacemaking process, but actually would be detrimental."

Carter had proposed that Khalil, who is subordinate to Egyptian President Anwar Sadat, meet with Begin, who is Israel's head of government and most powerful official. When the Israeli Cabinet, in a stinging rebuff, turned down the invitation, Carter immediately invited Begin to Washington for personal talks.

When asked today how he would respond if Carter tries to apply pressure, Begin replied, "I don't think President Carter will use pressure.I shall say very clearly, if pressure is used against us, we shall reject it."

Begin, in remarks to reporters after the Cabinet routinely approved his visit to Washington, repeatedly alluded to "new Egyptian demands," which he said the United States supports. The demands, Begin asserted, contradict the original Camp David agreements.

"There is indeed a very extreme, new attitude of the Egyptians toward the problem of the peace treaty. Had we accepted those proposals, let me say, ti wouldn't be a peace treaty at all. I would absolutely call it a war treaty, and in wars you don't need treaties, you need guns," Begin said.

Begin again refused to spell out what he sees as new Egyptian demands. But Israeli sources said they would:

Separate the Gaza Strip from the question of autonomy for the occupied West Bank of the Jordan River, with an implementation target date for Gaza. This, according to Israeli officials, calls into question Egypt's sincerity over West Bank Palestinian self-rule.

Establish an Egyptian police garrison and laison office in Gaza, with administrative control in the hands of Egyptian officers instead of Palestinians.

Require the release of Palestinian political prisoners, which Israel has adamantly refused to do on security grounds.

Provide for an exchange of ambassadors only after a comprehensive settlement is reached, rather than after Israel's withdrawal from half the Sinai Peninsula.

Give priority to Egypt's mutual defense treaty obligations to other Arab states, rather than to the Israeli-Egyptian treaty. According to the Israelis, if Syria attacked the Golan Heights, Egypt would have the right to attack Israel.

Begin referred obliquely to the stalemate over "priority of treaty obligations" when he said today, "That we should write in the possibility of a breach of the treaty in the treaty itself is absurd."

Th othe sticking points remain treaty clused that would link the separate Egyptian-Israeli provision to a solution of the Palestinian question, and a fixed timetable for implementing autonomy for West Bank and Gaza Arabs.

Begin is to leave here early Thursday morning. The meeting with Carter is expected to start Friday.