Egyptian President Hosni Mubarak urged President Reagan yesterday to begin talking with the Palestine Liberation Organization and permit U.S. officials to meet with a Jordanian-Palestinian delegation so Jordan's King Hussein can enter peace talks with Israel.

Mubarak, meeting with Reagan a week before Hussein arrives here next Monday, was repeating a plea that he made here in March.

After yesterday's meeting, however, U.S. officials said the United States will not deal with the PLO until it explicitly recognizes Israel's right to exist and accepts U.N. Security Council resolutions 242 and 338, which cover that point.

Hussein and PLO Chairman Yasser Arafat agreed in February on a proposal for moving toward revived Mideast peace talks if the United States meets with a joint delegation.

But the administration has insisted that the meeting be a prelude to direct negotiations with Israel, and Hussein has balked at making an unequivocal commitment to that.

Mubarak strongly supports the Hussein-Arafat proposal, and U.S. officials said he tried yesterday to "soften us up in advance of Hussein's visit by stressing that time is likely to run out unless the United States takes some initiatives to keep the process alive."

The administration also is concerned that lack of movement on the issue endangers its hope for progress toward peace talks and congressional approval of a related major arms sale to Jordan.

The officials said Mubarak was told that Hussein must show greater flexibility about talking with Israel if progress is to be made.

Despite signs of continuing stalemate, a senior U.S. official, who briefed reporters after yesterday's meeting, insisted, "The situation is not bleak."

The official, who could not be identified under the rules of the briefing, said Mubarak informed Reagan of his recent talks with Hussein.

While the official said Mubarak "made plain that he thinks time is wasting and is anxious that the process be given a push," the official would not discuss whether the Egyptian leader had brought any new proposals from Hussein.

Instead, the official said, the United States is reluctant to "preview" what Hussein might say when he speaks to the U.N. General Assembly Friday and at the White House next week.

According to the official, Mubarak reiterated Arab contentions that the PLO has implicitly accepted U.S. terms for a dialogue. That was a reference to statements by Hussein and other Arab spokesmen that, as part of a dialogue, the PLO would be prepared to recognize "all pertinent U.N. resolutions."

"We have never heard this explicitly from the PLO," the official said.

He stressed that the phrase "pertinent U.N. resolutions" is too vague to meet U.S. criteria for dealing with the PLO and added: "We want it to be more explicit."

In addition to discussing the peace process, Mubarak complained that high interest payments on military sales credits extended to Egypt impose severe additional burdens on the hard-pressed Egyptian economy.

While acknowledging that the situation is difficult for Egypt, the senior official noted that debt problems stemming from repayment of U.S. military aid loans affect many countries and cannot be eased without increasing the U.S. budget deficit. Only Israel receives more U.S. aid than Egypt.

Before going to the White House, Mubarak discussed Egyptian military needs with Defense Secretary Caspar W. Weinberger.

After meeting Reagan, he joined Secretary of State George P. Shultz and Egyptian Foreign Minister Esmet Meguid at the State Department to continue discussing regional and bilateral problems.