A prominent aide to Palestine Liberation Organization leader Yasser Arafat is in Washington to try to persuade the Reagan administration to help bring about a broad Middle East settlement with self-determination for the Palestinians.

Nabil Shaath, a leading member of the Palestine National Council -- the equivalent of a parliament-in-exile -- said in an interview that he was meeting members of Congress only, since the United States does not recognize the PLO and prohibits meetings between administration officials and PLO members.

He said Egypt and Saudi Arabia were mediating between the PLO and Reagan officials.

In London, the chairman of the Palestine National Council's foreign affairs committee, Kamal Hassan, urged the United States to begin an "immediate dialogue" for peace and warned that a solution "must be very, very quick" if renewed violence is to be avoided, United Press International reported. He said peace depended on international recognition of Palestine's right to exist, in particular by Washington.

Reacting to hints from State Department officials that U.S. Middle East policy will focus on safeguarding U.S. interests, Shaath said this would be an improvement. Eight weeks of fierce fighting in Lebanon, he believes, have brought the United States closer to linking its interests to a long-term settlement.

That change remains confined to perceptions rather than policy, Shaath said, adding that he expected a U.S. response to the PLO's first call for it to play peace-maker.

Despite the PLO leadership's initial disappointment that Palestinian fighters being evacuated from Beirut are not heading for Cairo, the PLO sees improvement in Egyptian-Saudi relations and possible coordination on the Palestinian issue as a goal, the Harvard-educated Shaath said.

Egyptian President Hosni Mubarak's weak point is that "he has not taken the steps needed to return to the Arab fold," Shaath said.

While Arafat reportedly intends initially to be based in Tunisia, Shaath said that the PLO chairman would be shuttling among Tunisia, Syria, Jordan and Egypt and that he planned to travel until he determined a new site for a permanent PLO headquarters.