US tries to cool three Mideast hot spots

In three areas of the Middle East, the United States is pressing ahead with new peace initiatives.

But in each case, the outcome is far from certain - and subject to many influences beyond American control.

* In the Iran-Iraq conflict, the Reagan administration is encouraging Islamic and nonaligned leaders to mediate in the hope of averting a spillover of the war into friendly, oil-producing Arab states. But the US does not have normal relations with either Iran or Iraq. Its direct influence is extremely limited.

* In shattered Lebanon, the US is proposing, among other things, a strengthening of the central government and a resolution of other problems at the root of the conflict. President Reagan is dispatching his special envoy, Philip Habib, to the Middle East next week to work to that end. But the Lebanon cease-fire remains fragile, subject to a major escalation of violence at almost any time.

* In Israel and Egypt, the US is pushing for an agreement on Palestinian ''autonomy.'' Israeli officials say that relations between the US and Israel are now on the mend following a period of tensions and disagreements over a number of issues. But the US and Israel still have much work to do to reestablish a common base for moving on to an agreement with Egypt. In anticipation of Israeli Prime Minister Menachem Begin's visit here June 21, the Reagan administration is giving priority to measures that would restore Israeli confidence in the US.

Until ''confidence building'' measures are carried out, Israeli officials say , speculation about a three-way summit meeting, bringing together President Reagan, Prime Minister Begin, and Egyptian President Hosni Mubarak, is probably premature.

It is in the Arab-Israeli conflict that the United States has by far the greatest influence. But in announcing a new push toward Palestinian autonomy in a speech in Chicago on May 26, Secretary of State Alexander M. Haig Jr. has thus far failed to elicit much of a response from the parties concerned. The reaction from Palestinians on the occupied West Bank of the Jordan appears so far to have been largely negative.

As far as the Israelis are concerned, the atmosphere definitely improved when the US Congress decided recently to grant Israel additional financial aid. At the end of Prime Minister Begin's visit here, the Reagan administration is expected to agree to revive now-suspended agreements that would strengthen Israel's defense industry.

When it comes to the Arabs, however, the United States faces problems on a number of fronts. Harold Saunders, assistant secretary of state for Near Eastern affairs under the Carter administration and now a senior fellow with the American Enterprise Institute, says he thinks that underlying these problems throughout the Middle East is an American credibility problem. He stresses that this problem did not begin with the Reagan administration but goes back several years.

As Mr. Saunders sees it, the credibility problem could be overcome if the US showed that it had ''a clear-cut sense of direction and a strong strategy'' for pursuing its objectives in the Middle East.

But in an interview with the Voice of America on June 2, Dr. Saunders also noted that there are limits to what American influence can accomplish in the Middle East. Concerning the Habib mission to Lebanon and the Iran-Iraq war, for example, he said:

''Problems in the Middle East are often so complex that there is . . . no single act by any power, even a superpower, which is going to provide the solution. What the large power, or the individual from outside, such as Ambassador Habib, can do is to move expertly and resolutely in a complex situation to help to bring out of it a sense of direction. He can help provide people in that complicated situation with a sense of communication, with a sense of emerging common purpose.

''In a situation like the Iran-Iraq war, it's unlikely that an outside power like the United States can have decisive influence. . . . What the US has been able to do in the past in situations like this is to serve as a stimulus - in some ways as a catalyst - among those powers who do have some influence in the situation.''

State Department officials say that is precisely what the US is now doing. According to one official, the administration is ''urging anyone who has influence'' to try to bring the Iran-Iraq conflict to a peaceful end. It is calling on members of the Islamic Conference and of the non-aligned movement - and Algeria in particular - to play a mediating role.

Some Middle East experts think it remarkable that the Lebanon ceasefire Habib helped to arrange has held for as long as it has - more than 10 months.

When it comes to Lebanon, Ambassador Habib, in keeping with his usual style, is holding any new ideas he may have close to his vest.

But the Palestinian side is not enamored with the direction US policy has taken under the Reagan administration. After discussions with several State Department officials in Washington this week, two West Bank mayors who had been expelled from Israel in 1980, Muhammad Milhem and Fahd Qawasmeh, spoke pessimistically about the prospects for Arab-Israeli peace.