Nicosia, Cyprus — President Reagan's ''fresh start'' initiative for the Middle East has slowly gained momentum over the past three months. And his proposals for peace are causing all parties to the Arab-Israeli conflict to adjust their positions:
* The moderate Arab nations are interested, but cautious about embracing it.
* The Palestine Liberation Organization and hard-line Arab states are negative, but not completely.
* Israel is defiant, but the Reagan administration is trying to bring it around.
The President's Mideast plan promises security for Israel and calls for Israeli withdrawal from the West Bank and Gaza (though perhaps not total withdrawal), negotiations over the status of Jerusalem, and Palestinian ''self-rule in association with Jordan.''
This proposal has supplanted the Camp David accords as the centerpiece of American Mideast diplomacy. US diplomats in the region have been directed to lobby intensively for the Reagan plan. European powers have let the Reagan plan take the lead over their Venice Declaration of 1980. And many moderate leaders in the 21-member Arab League back the Reagan plan in principle, though they still advocate their own plan, articulated Sept. 9 at the summit in Fez, Morocco.
By far the most negative to the Reagan plan, however, are hard-liners Israel, Syria, and the PLO. Because of their rejection so far, their emotional attachment to the issue, and their predilection for armed combat, these three powers cannot be ignored. They are spoilers - and without a significant change of tone from them, the Reagan plan is dead in the water.
Both Washington and moderate Arabs realize that the rejectionists in Israel and the Arab world must be coaxed, nudged, and perhaps bullied into compromise. The US may have the daunting task of delivering the support of Israel, changing the mind of the Menachem Begin government, and ending the 15-year occupation of the West Bank and Gaza (with the huge capital investment Israel has made there). But moderate Arabs behind the leadership of Saudi Arabia, Jordan, and Egypt have the equally challenging job of bringing around PLO and radical governments - most importantly, Syria - to accepting Israel's right to exist, and ending 35 years of Arab belligerency.
Unlike Camp David, the Reagan plan so far does not have the strength of formal treaties and person-to-person goodwill behind it. It is just a plan, not yet the ''framework for peace'' that Camp David has been. But as with Camp David , American prestige in the Middle East is bound up with the success of the Reagan plan. At the least, the plan is a measure of US sincerity in a skeptical region.
Mr. Reagan's proposal has gone some way toward redeeming American credibility after what was seen in the Middle East as tacit American support for Israel's invasion of Lebanon last summer.
The work of US diplomats Philip Habib and Morris Draper in trying to sell the plan has been viewed among moderate Arabs as some proof that the US wants to solve the Palestinian problem by freeing the West Bank and Gaza from Israeli occupation. Washington is trying to break the ''who-talks-to-whom'' deadlock - a precondition to negotiations. The PLO does not recognize Israel, nor Israel the PLO, and the US will not talk with the PLO until it changes its attitude.
The State Department is considering a plan whereby if the PLO recognizes Israel, the US enters discussions with the PLO immediately. This, it is believed , would protect PLO moderates who stick their necks out in delivering the radicals - and it would show the benefit of a conciliatory line.
Even so, the PLO would have to take the giant step of recognizing Israel first. Many Arab leaders have been urging PLO leader Yasser Arafat to do this, but radicals within the PLO are preventing it. And even if the PLO does recognize Israel, Begin is not likely to recognize - and talk with - the PLO.
But US diplomats believe moderates within Israel, the PLO, and Syria may yet be found. Israel's Labor Party has endorsed the Reagan plan in principle. State Department officials believe Begin or a successor might eventually be prevailed upon. They say this is the optimum choice, since changing the mind of a hard-line prime minister (with the opposition already amenable) ensures Israeli commitment to peace.
Nor is the Arab side of the equation completely frozen. Within the PLO, Mr. Arafat has expressed interest in the Reagan plan. And even as Syria officially sends out negative signals, President Hafez Assad has opened his door many times to Messrs. Habib and Draper to discuss the plan.
Among Arab moderates, Egypt is the most vocal advocate of the Reagan plan. President Hosni Mubarak last month reminded other Arab leaders that to reject it would ''mean that the expected movement of a great power had been frozen without good reason.''
But it is Jordan, not Egypt, that would be in the most precarious positon under the Reagan plan. King Hussein, who meets with Reagan Dec. 21, nevertheless has shown considerable interest. Besides guarded early support, the King, during frequent meetings with Mr. Arafat over the past two months, has urged the PLO leader to seize the moment and work with this new proposal. Under an Arab League agreement, however, the PLO, not King Hussein, can negotiate the future of Israeli-held territory. The PLO has been reticent to delegate this power to the King.
The PLO demands a totally independent Palestinian state in Israeli-held territory with Arab east Jerusalem as its capital. A recent PLO Central Committee meeting reacted negatively to the Reagan plan. Even Mr. Arafat in his recent public statements has distanced himself from compromise.
Nor does Israel seem ready to halt annexation of the West Bank and Gaza. New West Bank settlements were announced recently.