President Reagan assured Jordan's King Hussein yesterday of his "deep commitment" to keep pursuing the Mideast peace initiative that he announced on Sept. 1, and he said that "we share a sense of urgency" about the need for progress toward broadening the peace process.

Hussein replied that he, too, has a "long-lived commitment for the establishment of a just and durable peace . . . ." But sources familiar with their talks at the White House said the king made no promises about entering the peace talks and stressed that it will be extremely difficult for him unless the United States can get Israel to halt or slow its establishment of settlements in the occupied West Bank.

The sources added that the settlements problem will be discussed at length by U.S. and Jordanian officials before Reagan and Hussein meet again before the king's departure on Thursday.

The aim, as one source put it, "will be to discuss the art of the possible" in finding ways to ease Arab concern about the settlements. However, he and others stressed that the process is not expected to advance far enough to produce "any dramatic breakthroughs or announcements" while Hussein is here.

These sources said that even if the United States decides to press Israeli Prime Minister Menachem Begin anew for a freeze or slowdown on settlements, Reagan won't have an effective forum until Begin meets with him here in January or February.

The sources acknowledged that this further delay works against the "sense of urgency" mentioned by Reagan and is likely to increase concern that his initiative will be overwhelmed by inaction.

However, while acknowledging that the danger is real, the sources also said that the administration believes it has until spring to demonstrate whether it can bring about a broadened and revitalized peace process.

Reagan was smiling and in an obviously upbeat mood when he and Hussein emerged from a two-hour meeting to talk briefly with reporters. The king had been seeking Reagan's personal assurance that he intends to stay with his initiative despite Begin's rejection of the U.S. proposals, and the president said pointedly:

"I told the king of my personal commitment to see peace in the Middle East become a true and lasting reality, and of my equally deep commitment to the proposals that we made Sept. 1 to Israel, to the Palestinians and to the Arab states."

He then referred indirectly to the initiative's central premise, which calls for the West Bank and Gaza Strip to gain eventual independence "in association with Jordan." As a vital step toward that end, the United States wants Hussein to join negotiations over the status of these territories as a representative of the Palestinians; the king is seeking the endorsement of the Palestine Liberation Organization to assume that role.

"His majesty eloquently described his vision of peace and reviewed for us what he's been doing to help give peace a chance to take root--particularly his efforts to encourage the Palestinians to join him in efforts to take bold steps toward peace," Reagan said.

Khalid Hassan, a key aide to PLO leader Yasser Arafat, has been staying at Hussein's hotel during the king's visit, and diplomatic sources said he was being kept informed of the discussions by the Jordanian delegation. The United States does not recognize the PLO and refuses to deal with it directly.

A senior administration official, who briefed reporters on condition that he not be identified, noted that Hussein's efforts to reach an agreement with the PLO are an important element in determining whether the king elects to come into the peace process. But, the official said, "How fast and how far they are going to go is a question I can't answer."

The same official also acknowledged that Hussein had put great emphasis on the settlements issue as a test of whether Israel is willing to negotiate about the West Bank and Gaza on the basis of a formula that envisions returning them to Arab control in exchange for peace and Arab recognition of the Jewish state.

Other sources said later that, while Hussein did not make it an explicit condition, he made clear that it would be virtually impossible for him to join the peace talks without progress toward an Israeli withdrawal from Lebanon and concessions on the settlements.

On the Lebanon question, Reagan's special Mideast representative, Philip C. Habib, told the president yesterday that he expects Israeli-Lebanese talks to begin within a few days. Habib also participated in the meeting with Hussein, and the senior official said he will head the U.S. side in the talks here with Jordanian officials.

Other sources said those talks are expected to focus on the settlements question. As one put it, "Unless that issue can be removed as a major stumbling block, there's a question about whether there would be any point in proceeding to broadened negotiations."

The senior official, answering questions about Jordan's desire for advanced U.S. weaponry, said no formal requests had been made by Hussein. The administration is known to be willing to provide F20 jet fighters and shoulder-fired Stinger missiles but -- because of congressional opposition -- has held back on commitments to sell the more advanced F16 fighter-bomber and mobile Hawk ground-to-air missiles.

The sources said the Jordanians had agreed to hold off their requests for the more advanced equipment. While Hussein is expected to accept the F20s and Stingers, an announcement is unlikely until after the new Congress convenes on Jan. 3.