King Hussein of Jordan and Chairman Yasser Arafat of the Palestine Liberation Organization began critical discussions today to save their moribund, nearly year-old Middle East peace initiative.

The king was expected to inform Arafat about his recent meeting in London with Richard W. Murphy, assistant secretary of state for Near East affairs, and the U.S. envoy's discussions in the Netherlands and Britain with Israeli Prime Minister Shimon Peres.

Two aides to Murphy, Wat Cluverius and Roscoe Suddarth, were here amid speculation that their role was to convey U.S. views in the event that Arafat and Hussein reach agreement on how to move forward in negotiations with Israel. Suddarth met this evening with Hussein and Prime Minister Zaid Rifai, officials said.

No details emerged from a formal luncheon of high-ranking PLO and Jordanian officials that was followed this evening by a private meeting between the two leaders at the royal palace.

PLO, Jordanian and West Bank officials all discouraged Peres' suggestion that Hussein would drop the PLO and start peace talks with West Bank political leaders instead.

In an interview here, Zafer Masri, recently appointed by the Israeli occupation authorities as mayor of the West Bank city of Nablus, rejected suggestions of West Bank cooperation in such a plan with a curt "No!"

With Congress threatening to scuttle deferred arms sales to Jordan unless peace talks with Israel begin by March 1 and with Peres rumored to be seeking a late spring election, analysts suggested that Murphy's talks may have found some last-minute formula to break the deadlock.

Such upbeat suggestions appeared principally based on officially unstated, but clear, U.S. hopes that progress toward peace talks could help Peres call -- and win -- elections before he must otherwise hand over power to his hard-line Likud coalition partners.

Barring such a breakthrough, diplomats and analysts here believe that the current meetings, the first since Arafat visited here in November, would spell the effective end of their initiative of last Feb. 11.

Palestinian sources did little to discourage such pessimistic appraisals following a meeting in Baghdad, Iraq, 10 days ago of Arafat's loyalists on the divided PLO Executive Committee and his mainstream Fatah organization.

But sources reiterated Arafat's refusal to accept United Nations Security Council Resolutions 242 and 338 as the king has demanded if the peace initiative is to go forward. Those resolutions recognize Israel's right to exist within secure borders in exchange for the return of land the Jewish state occupied during the 1967 Arab-Israeli War.

Traditionally, the PLO has rejected those resolutions because they mention only a refugee problem without reference to the Palestinians or their political rights.

Such seemingly insurmountable obstacles have encouraged speculation that all regional parties -- the PLO, Jordan, Israel and Syria -- already are preparing to present the best possible face in the eventual demise of the Feb. 11 initiative.

Thus, Peres, short of actually being able to start peace talks before an election campaign, could claim that during his recent European tour he demonstrated his willingness to explore future initiatives.

King Hussein already has gone a long way to repair a decade of steadily deteriorating relations with Syria by traveling to Damascus last month to meet President Hafez Assad, increasingly viewed as the strongest leader in the Arab world.

Assad remains steadfastly opposed to any participation in the peace process by Arafat, whom he expelled from Damascus in 1983.

Arafat and other PLO leaders have voiced fears that rapprochement between Amman and Damascus could be at the expense of their relations with Jordan. However, analysts noted an improvement in relations between Syria and Arafat's wing of the PLO with the cessation of mutual propaganda attacks.

Arafat is expected to blame any breakdown in relations with the king on the United States and Israel for not showing more flexibility toward the PLO.

However, optimists still held out hope that Murphy had succeeded in extracting further compromises and wording from Israel to make it easier for the PLO to meet the necessary conditions for participating.

For example, instead of having recognized the right of Israel to exist -- in PLO eyes, tantamount to negation of their own claims to national rights -- language worked out by the United States and accepted by Peres now stipulates only that the PLO state its willingness to negotiate with the Israeli government.

Similarly, the United States and Israel have dropped their refusal to hold any peace talks under the umbrella of an international conference. Jordan has insisted on such a conference in part to meet demands from Syria and its Soviet ally.