Beirut — After months of stagnation, the Middle East is bustling with activity, in turn sparking cautious optimism about a new peace initiative. But at the same time, there are serious divisions among major parties to the Arab-Israeli conflict that could block efforts before they even get off the ground.
Over the past two weeks:
* The 18-month rebellion within the Palestine Liberation Organization has been at least partially resolved. The moderate majority endorsed the leadership of chairman Yasser Arafat at a long-delayed summit of the PLO's parliament-in-exile. The mutiny by hard-liners had paralyzed the PLO - and various peace plans.
* At the Palestinian conference, Jordan's King Hussein proposed that the PLO and the kingdom join together, as equal partners, in seeking a settlement of the 36-year conflict with Israel over a Palestinian homeland.
* The Jordanian monarch then paid an official visit to Egypt, the first by a major Arab leader since Cairo agreed to negotiations with Israel seven years ago. During three days of talks, the King won support from Egyptian President Hosni Mubarak for a United Nations-sponsored international summit - including Israel, the PLO, and both superpowers - as a forum for resolution of the Arab-Israeli conflict. They jointly appealed to the Arab world to accept the King's initiative.
* Despite recent claims from Washington that the positions of the major parties were too far apart to warrant American mediation, US Assistant Secretary of State Richard Murphy is launching a new round of shuttle diplomacy in the region this week. Last month the US and Iraq renewed formal relations, further aligning Iraq with the Arab moderates.
Within the Arab world, there were abundant signals that moderate nations were actively trying to revive deadlocked peace efforts during the ''four-year window'' of President Reagan's second term.
But two major obstacles face the moderates.
First, Israeli Prime Minister Shimon Peres on Monday rejected the call for an international conference, adding that Israel would not negotiate directly with the PLO. But he did indicate a willingness to negotiate with Palestinians not associated with the PLO. ''If Jordan is interested in peace, and peace is a mutual interest,'' he said, ''we must open negotiations immediately and conduct them with patience.'
Second, Syria has harshly criticized Jordan's moves as ''treason'' and declared that the Arafat-led PLO carried no legitimacy and that its council resolutions were thus not valid.
Hard-line Syria has often played spoiler to Middle East peace efforts. But Western envoys suggest that President Hafez Assad does not oppose a settlement with Israel. His rejectionist position instead reflects his almost desperate desire to be the chief Arab negotiator.
It is this goal that led Mr. Assad, in his effort to gain control of the ''Palestinian card,'' to back a rebellion against Arafat, diplomats say. It was also behind his campaign to get the US out of Lebanon, for fear that a settlement with Israel there would lead to broader negotiations among the US, moderate Arabs, and Israel.
Indeed, until the recent flurry of activity, Syria appeared to be in the driver's seat. Assad had taken over from the US in dominating Lebanese negotiations. He controlled key elements in the PLO and he had several Western and Arab nations courting him or seeking his council, including French President Francois Mitterrand just last week.
As Arab envoys admit, the Syrian leader, who has been variously described as ''brilliant'' and ''ruthless,'' is not likely to let the moderates steal the limelight. During the PLO summit in Jordan last week, Palestinian and Jordanian sources conceded that they expected violence in response to their political moves.
For the Jordanian-led effort to make any headway, two steps are crucial. One is broad unity within the Arab League, whose summit last month in Riyadh, Saudi Arabia, was postponed because of serious rifts. The Arab League is one forum where Syria can play spoiler, as it did at the 1981 conference in Fez, Morocco. Syria did not show up, forcing cancellation of the talks. Acceptance of Saudi Arabia's eight-point peace plan - the ''Fez plan'' - was delayed for a full year.
The second step is US involvement. Jordanian Prime Minister Ahmed Obeidat appealed to the Reagan administration Monday to shoulder its responsibility as a superpower in pressing Israel to give up its occupied territories.
All the major front-line states have conceded that it will require major pressure from the US to get Israel to make territorial concessions. The recent massive financial aid from Washington, expected to grow still larger and designed to ease Israel's economic crisis, offers new leverage, Arab sources contend.
The moderate bloc is also hoping that President Reagan, no longer forced to play to various lobbies for reelection, will be in a stronger position to maneuver.
So far, it appears that the main purpose of Mr. Murphy's visit is to help end the deadlock in Lebanese-Israeli talks on withdrawal of Israeli forces from Lebanon. But there is strong speculation that he will also travel to Cairo and Amman, Jordan, to probe deeper into the moderates' intentions.
A high-powered Arab noted recently that there was, indeed, a new impression of momentum in the region. But reflecting the caution that follows 36 years of failed peace efforts, he noted that it may be more an impression than real momentum.