Vasser Arafat and Jordan's King Hussein abruptly recessed their intense negotiations over President Reagan's Middle East peace initiative this morning, and the Palestine Liberation Organization leader flew to Kuwait.

But Arafat said later that the interlude did not mean obstacles are impeding an accord to allow Hussein to enter peace negotiations. Reagan has called for the king to represent the Palestinians in talks with Israel.

"King Hussein and I are agreed on what is good for both sides," Arafat, in his strongest statement on the progress in the three days of private talks with the king, told a reporter for The Associated Press when he arrived in Kuwait.

Arafat's advisers and analysts here suggested that he would be gone no longer than 72 hours. He was seeking a brief cooling-off period away from Hussein, who reportedly is putting pressure on the PLO leader, they said.

Observers here also said they expect Arafat to stop in Saudi Arabia to see King Fahd, who reportedly has played an important behind-the-scenes role in the negotiations.

These observers said Arafat apparently felt he needed Fahd's help in dealing with Hussein and to help him with the Syrians, who have issued strong rhetorical blasts about the negotiations.

State Department spokesman John Hughes, reflecting concern in the Reagan administration that time is running out for the U.S. peace plan, called in Washington for "a prompt move" by Hussein, with Palestinian backing, AP reported.

Hughes praised the king's efforts so far, but he appealed for "others as well to recognize that this is a unique moment which must be seized before it is lost." He said there "is a sense that those talks (in Amman) are coming to a conclusion."

There was strong optimism here about the progress of the talks.

"We get the feeling of an impending something," said a European diplomat. "I caution, however, that in the Arab world that often doesn't happen."

Both radical and moderate PLO leaders went to great lengths to reassure reporters that Arafat's departure did not mean the talks had collapsed.

An aide at Hussein's royal palace telephoned journalists at their hotel to dissuade those who earlier booked flghts out today to remain, saying he expected "important news" in coming days.

An official press communique, apparently approved jointly by Hussein and Arafat, described the talks as taking place in a "brotherly atmosphere and a constructive spirit."

"The two sides agreed to continue their discussions after Mr. Arafat's return in the near future," the statement said.

A PLO moderate said, "There is general agreement on many, many things. I think they haven't worded the final communique very carefully. That is the reason for the delay."

Radical PLO members appeared to want to put some distance between themselves and the negotiations but even the most outspoken opponents stressed that this did not mean the PLO was splitting.

It was unclear what issues had been resolved in the private talks and what remained outstanding.

The issue of who would speak for the Palestinians in the peace negotiations was not a stumbling block, said one PLO leader. He suggested that the PLO might agree to an arrangement similar to a formula used in a recent Arab League delegation to London where Arafat designated a Palestinian historian who holds no office in the PLO as the group's representative.