U.S. and Israeli officials are trying to arrange an urgent trip to Washington by Foreign Minister Moshe Dayan to resolve the acrimonious squabble about an international peace-keeping force for the Sinai peninsula, U.S. sources said.

Friction between the two nations continued to grow yesterday, however. Acting despite strong objections from Israel, the State Department announced that the United States plans to sell as many as 300 sophisticated M60 tanks to Jordan.

And testimony given on Middle East policy to a House subcommittee by Assistant Secretary of State Harold H. Saunders was not calculated to soothe Israeli nerves. Saunders put fresh emphasis on the U.S. stand toward Palestinian nationalism as a factor in U.S. relations with other Arab nations, which count in their ranks some of the world's largest oil exporters.

The frequently turbulent relations between the governments of Prime Minister Menachem Begin and President Carter have been slumping again since Sunday, when the Israeli cabinet suddenly rejected a U.S. proposal on policing the Egyptian-Israeli peace treaty.

Administration officials have sought to minimize the importance of the Israeli action and of the dispute it has created. But Dayan and other Israeli officials say the dispute throws into doubt the Carter administration's good faith and its intention to carry out the treaty obligations Carter boldly accepted in March.

With Begin still hospitalized with what has been described as a small blood clot in an artery leading to his brain, Dayan has taken charge of the peacekeeping problem and has taken a hard line that appears to puzzle U.S. officials.

Dayan, now in the Netherlands, has signaled a desire to come to Washington, and the White House is preparing an invitation, administration sources said. Israeli officials in Washington said they had no information about the invitation.

There was sharp dispute even over the details of the effort to arrange the fence-mending meeting in Washington. U.S. officials said yesterday that Dayan had originally suggested that Secretary of State Cyrus R. Vance was reported to have rejected immediately.

Israeli officials here emphatically denied that Israel was seeking an urgent meeting and repeated Dayan's assertions that the United States was deliberately refusing to live up to its obligation to form a U.S.-sponsored multinational peace-keeping force for the Sinai.

Speaking to reporters at a daily news briefing, State Department spokesman Hodding Carter said that neither Vance nor President Carter's new special Middle East negotiator, Robert S. Strauss, had any plans to go to the Middle East to discuss the peacekeeping force.

Strauss left Washington yesterday for a long-planned vacation and his role, if any, in the projected meetings here with Dayan and the dispute over the Sinai force was not immediately clear.

Strauss saw his previous job as the White House's special trade negotiator come to an end yesterday in a ceremony in the Rose Garden, during which President Carter signed the international trade bill overwhelmingly approved by Congress last week.

U.S. officials suggest privately that they expect Dayan to come to Washington prepared for political bargaining in which the Sinai peace-keeping question may be only one factor. But they say they have no clear idea of what Dayan may be after.

The dispute centers on the expiration last Tuesday of the U.N. Emergency Force (UNEF, a 4,000-man unit that has policed Egyptian and Israeli disengagement agreements in the Sinai since 1974. Begin, President Anwar Sadat of Egypt and Carter had hoped that UNEF would be allowed to continue and police the new treaty.

But under the threat of a Soviet veto, the United States decided not to go into the Security Council for an extension of UNEF. Instead, Washington and Moscow reached a private deal that would allow the U.N. Truce Supervisory Organisation (UNTSO) to be expanded and deployed into the Sinai to watch over the treaty.

"We have an understanding with all the members of the Security Council, including the Soviet Union, that the secretary general shall be free to establish the number of troops necessary and the equipment and placement necessary to carry out the functions which we spelled out in the treaty," a State Department official said at a news briefing Wednesday in the first semi-public description of the terms of the U.S.-Soviet accord.

Reports from U.S. and U.N. sources say that UNTSO might be expanded from 300 officers to 500 to 800. Israel has sharply criticized the U.S.-Soviet arrangement as insufficient.

In disclosing the tank sale to Jordan yesterday, Hodding Carter emphasized that King Hussein would not necessarily buy all of the 300 M60 tanks the administration is prepared to sell his government. Carter also stressed that each M60 would replace an older M48 tank, meaning there would be "no expansion of Jordanian tank units or the force structure," an assertion that Israeli officials immediately challenged.

The State Department spokesman said that because of the long U.S.-Jordanian military relationship, Jordan could be counted on to live up to its pledges not to build up a much larger tank force.

A U.S. official said that the M60 sale, which could be worth up to $300 million, would be "blended" into a pending Jordanian order of 275 British-manufactured Chieftan tanks so that Jordan would probably receive a total of 300 new tanks.

The testimony by Saunders, the expert, before the House subcommittee on Europe and the Middle East, was carefully balanced, and did not appear to mark any significant new policy departures.

But the nuance of several of his remarks about U.S. intentions to talk to the Palestine Liberation Organization if it publicly accepts Israel's right to exist did appear to put some points in a new light.

Stressing U.S. and Arab "interdependence," Saunders observed that "the Palestinian problem must be seen not only in the context of the Arab-Israeli negotiations but also in the context of the Arab world's need to deal honorably with the legitimate interest of a Palestinian community with sizable and influential numbers in the key Arab states."

Palestinian engineers and field workers play a key role in the oil industry in Kuwait, Saudi Arabia and other Arab petroleum exporting nations.

Asked about a U.S. commitment to Israel not to talk with the PLO as long as that organization does not accept U.N. Resolution 242 and provide other signs of recognition of Israel, Saunders said: "It is a sensitive political issue, and we're going to be dealing with that not as a legal issue but as an issue that must be resolved in the context of supporting the negotiating process."

Saying that there had been "an evolution" in some PLO attitudes toward Israel, Saunders agreed with the assessment of Rep. Lee Hamilton (D-Ind.), who said that Saunder's remarks indicated that the United States is "on the verge of a concerted effort to include Palestinians of all political stripes in the negotiating process."