A special envoy from the Reagan administration described his talks with President Hosni Mubarak today as "a good first step" in repairing relations with Egypt damaged by the U.S. interception of an Egyptian aircraft carrying Palestinian hijackers of the Achille Lauro cruise ship.

Deputy Secretary of State John C. Whitehead said he delivered a letter from President Reagan "that expressed his continuing commitment to close U.S.-Egyptian relations and his hope that we could put our recent differences behind us."

But Egyptian officials suggested after the almost two-hour meeting between Mubarak and Whitehead at Oruba Palace that they still want to see some American actions to back up the warm U.S. language.

"We view everything positively, but we shall wait and see," Osama Baz, Mubarak's top national security adviser, said today.

Another letter from Reagan to Mubarak was delivered eight days ago and described by U.S. officials then as "a very good first step."

Both Whitehead's prepared statement and Baz's remarks after the Mubarak meeting indicated that the main hope for movement toward repairing relations is a possible procedural breakthrough in the broader search for a Middle East peace settlement.

Whitehead said today that "much of our discussion focused on the peace process and the importance of moving forward soon toward direct negotiations within an appropriate context. We agreed that both our nations have important roles to play in accelerating that process."

Egypt and Jordan have been pressing for an international conference including the Soviet Union as a transitional framework leading to direct talks between Israel and a joint Jordanian-Palestinian delegation.

The United States has rejected proposals for such a conference, maintaining that it would be a grandstand for ideological posturing and that the Soviet Union should be excluded because it does not have diplomatic relations with Israel.

The Israeli bombing of Palestine Liberation Organization headquarters in Tunisia on Oct. 1 and events surrounding the hijacking of the Achille Lauro cruise ship appear to have sidetracked the peace process.

But senior Foreign Ministry officials have suggested that a U.S. concession on the international conference now would go far toward assuaging Egypt's anger over the interception of its plane and might help restore some life to a process they consider vital for the region's stability.

Baz, who sat in on the Mubarak-Whitehead meeting, said, "We did not get into specifics, but there was agreement that movement in this direction was needed."

It was reported in the Egyptian press today that Mubarak spoke with Jordan's King Hussein by telephone yesterday. No details were given.

The apparent American endorsement of Israel's Oct. 1 raid in Tunisia and the events surrounding the Oct. 7 hijacking of the Achille Lauro have badly frayed Washington's relations with three of its closest friends in the Mediterranean: Cairo, Rome and Tunis. Whitehead's mission has been to try to mollify leaders in all three capitals.

He arrived here Saturday night after a meeting with Italian Prime Minister Bettino Craxi and flew tonight to Tunis, where he is to meet Tuesday with President Habib Bourguiba.

During the past week, radical Egyptian students have taken to the streets in violent clashes with police unprecedented in the four years since president Anwar Sadat was assassinated.

As Mubarak approaches difficult domestic decisions about further price increases for basic goods in an increasingly austere economy, he considers his position badly undermined by the actions of his greatest friend and benefactor.

While the United States has viewed the interception of the Egyptian plane and the arrest of the hijackers in Italy as a triumph against terrorism, Egyptians view it as a slap in the face from a country with which they have had warm relations and on which they depend for more than $2 billion a year in vitally needed aid.

Whitehead repeated the U.S. position that intercepting the plane carrying the hijackers to the custody of PLO Chairman Yasser Arafat was "in no way directed against Egypt or its people, for whom all Americans have the deepest respect."

"We very much regret that developments took the course they did," he added. "Our only objective was to bring to justice criminals who had hijacked the ship, terrorized its passengers, murdered an American -- a crippled man in a wheelchair -- and threatened to murder others."

"We appreciate that Egypt's efforts in saving the lives of over 400 people helped ensure that the hijacking did not have a far more tragic result, and we are grateful for that," he said.

He and Mubarak agreed, he said, "that the unfortunate events of the last few weeks must not interfere in the close and vitally important relationships that bind our two great nations."