President Reagan told a high-level Arab delegation yesterday that Mideast peace requires new negotiations "in the very near future," and Morocco's King Hassan, in an apparent reference to Israel, assured the president that Arab goals include "coexistence" within the region.

Their public exchange followed a White House meeting where Hassan and the foreign ministers of five other Arab countries described to Reagan the views outlined in an eight-point declaration adopted last month by an Arab League summit meeting in Fez, Morocco.

At a background briefing later, a senior administration official characterized Hassan's remarks as "encouraging" for progress on the Middle East peace initiative launched by Reagan on Sept. 1 in hopes of resolving the Arab-Israeli conflict.

However, the official acknowledged that the meeting had produced no immediate breakthrough for U.S. hopes of getting the Arab nations to deal directly with Israel or to encourage King Hussein of Jordan to join the negotiations on an interim autonomy system for the Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip.

The core of Reagan's initiative calls for getting a five-year autonomy plan into operation and then proceeding to further negotiations that the United States envisions as granting the occupied territories eventual self-rule "in association with Jordan."

The official, who cannot be identified under the rules of the briefing, said Reagan had stressed to the Arab representatives that the urgency of the Middle East situation makes it imperative "to move to the negotiating table" and that the United States believes this can be done best if the Arab world supports Hussein's entry into the talks.

According to the official, Hassan, speaking for the delegation, reiterated the longstanding Arab position that the Palestine Liberation Organization is the only authorized spokesman for the Palestinian people, that Hussein's involvement can only come about through the agreement of the PLO and that discussions about this point currently are being pursued between Hussein and PLO Chairman Yasser Arafat.

"Based on what we heard, there is no reluctance to support Hussein, but it is with the qualification that it be done in the context of an agreement with the PLO," the official said.

In response to questions about when the talks between Jordan and the PLO might produce results, the official said, "No one gave us any ideas on timing." He added, though, that there were hints in the meeting that the Palestine National Council, which on paper is the supreme authority of the PLO, is expected to meet in four to six weeks with results "which might be very dramatic."

Asked what Hassan had meant by his reference to "coexistence," the official replied, "In the context of the discussions here, it was well understood that we were talking about a state called Israel and peace terms."

The Fez declaration, which calls for an independent Palestinian state under PLO leadership, is, on its face, a rejection of the Reagan initiative. However, U.S. officials have tended to regard it as an opening Arab negotiating move rather than an immutable position, and Washington was especially encouraged by one point that is widely regarded as implying Arab recognition of Israel's right to exist in exchange for satisfactory resolution of the Palestinian issue.

On Thursday, a senior State Department official, talking with reporters on background, said it was time for the Arabs "to come out of the closet" and state specifically whether they are willing to recognize Israel. However, the official at yesterday's briefing conceded that the Arabs are not yet willing to go that far.

"The measure is not whether the Americans are satisfied but whether there is a clearly and on-the-record stated Arab proposal to recognize and live in peace with Israel. That has not yet happened," the official said.

But, while the session made clear that months of further diplomatic maneuvering will be required to move the Middle East situation in the direction desired by the administration, the atmosphere yesterday was clearly upbeat and indicative of optimism on both the American and Arab sides.

Reagan, in taking leave of his guests, called the meeting "an important milestone along the road toward . . . security for the Arab states and security for Israel and a sense of identity for the Palestinian people."

Hassan, in his response, cited not only the Fez declaration but also Reagan's initiative and U.N. Security Council Resolutions 242 and 338 as jointly forming "a framework . . . to achieve our noble aim and objective which is peace and coexistence and construction for the welfare of the region and all mankind."

In addition to Morocco, those countries represented in the delegation were Jordan, Saudi Arabia, Syria, Algeria and Tunisia.