The Palestine Liberation Organization has agreed in principle to help finance a peace institute as settlement of a lawsuit by the family of Leon Klinghoffer, the wheelchair-bound Jewish American who was slain when terrorists hijacked the cruise ship Achille Lauro in 1985.

Klinghoffer, 69, was a passenger on the Italian vessel when terrorists belonging to an extremist PLO faction hijacked it in the Mediterranean Sea off Egypt for three days. He was shot and his body thrown overboard.

The killing triggered an international uproar that led to U.S. fighters forcing an Egyptian plane carrying the terrorist faction's leader, Mohammed Abul Abbas, to land in Italy.

However, U.S. military personnel were prevented from capturing Abbas by the Italian government, which intervened and, ignoring a U.S. extradition effort, sent him to safety in Yugoslavia.

The incident also caused the United States to break off attempts to open a dialogue with PLO Chairman Yasser Arafat because of his refusal to take action against Abbas, then a PLO governing board member.

However, the more recent peace accord between Israel and the PLO has created a new, friendly relationship between Arafat and the United States. Now the PLO apparently hopes to remove one of the lingering shadows over that relationship by coming to terms with Klinghoffer's survivors.

Last week, lawyers for the two sides sent a letter to Judge Louis L. Stanton of the U.S. District Court here saying they had reached a tentative settlement and were attempting to work out the details that would make it final and end the suit brought by Klinghoffer's two daughters, Ilsa and Lisa, against the PLO.

His wife, Marilyn, who also was taken hostage on the Achille Lauro, died in 1986.

The letter said the proposed settlement calls for creating an institute "designed for peace studies including prevention of terrorism" through scholarly research, teaching and publications. It said the institute would "memorialize the tragic death of Leon Klinghoffer as well as other victims of violence" and that his daughters "will perform a significant role" in its administration.

It added that Arafat supports the concept of the institute and that the PLO, or its successor in the emerging Palestinian authority in the West Bank and Gaza Strip, would make an initial contribution. Other funding sources also would be sought.

If the agreement is finalized, further litigation against the PLO by the Klinghoffers and the New Jersey travel agency that booked the cruise "will not be necessary," according to the letter from Ramsey Clark, lawyer for the PLO, and Jay Fischer, the plaintiffs' attorney.

Letty Simon, spokeswoman for the Klinghoffer daughters, said the judge had set a mid-February deadline for reaching a final agreement.

In its initial legal responses, the PLO had contended it was not responsible for the hijacking because it was carried out by a group outside the PLO factions controlled by Arafat. However, Abbas had supported Arafat in internal PLO political squabbles and retained his position as a PLO governing board member after the hijacking.

More recently, his opposition to reconciliation with Israel led to a rift with Arafat and his removal from the governing board. CAPTION: LEON KLINGHOFFER