President Reagan has given himself a renewed challenge to make quiet diplomacy work for Mideast peace. He did so in effect by conspicuously forgoing the other options invited by questions during his first news conference since the Beirut massacre.
* Mr. Reagan could have put public pressure on the conflicting parties in Lebanon by stating a deadline on the stay of US Marines as part of the new multinational force there. After all, he had originally said they would be deployed for only a limited period. Now, instead of specifying limits, he said they would remain until all foreign forces withdraw and the Lebanon government tells them when ''they can go home.''
Will the prospect of an indefinite stay by the Marines encourage the Israeli and Syrian troops to leave and the Lebanese government to pull itself together and take charge? Or will feet drag under the lingering umbrella of the superpower and its European colleagues?
This is where the American President challenges himself to speed the process through vigorous diplomacy to prevent a mini-Vietnam quagmire. If he doesn't, he will doubtless have Congress to contend with.
* Mr. Reagan could have put public pressure on the Israeli invaders of Lebanon being held responsible by his own State Department for allowing the massacre to happen. Instead, he expressed no anguish over the atrocities and went out of his way to be conciliatory toward Prime Minister Begin and Israel as ''our ally.''
If he is bringing any pressure to bear on Israel, it must be in private as President Eisenhower did when he successfully threatened sanctions during the Suez crisis of 1956. Again, unless some progress is achieved somehow, Mr. Reagan is likely to hear more from members of Congress threatening sanctions of their own.
To be sure, the US President did not seize the opportunity for condemnation of those ''Christian'' Phalangist forces that perpetrated the massacre either. There was no nudging of Lebanon's new president, Amin Gemayal, himself a Phalangist, to get to the bottom of the tragedy and prevent any repetition of it. Here, too, the task is evidently left for quiet diplomacy.
But Mr. Reagan's omission of public pressure was more noticed in the case of Israel, the invading power and the beneficiary of huge amounts of US aid. To stress the concept of Israel as an ''ally'' now must at least puzzle an American public cooling toward Israel's conduct after decades of fast friendship.
The friendship with the Israeli people will, of course, continue. But Israel has never been an ally of the United States in the formal sense of NATO partners , for example. Nor have the two countries behaved as allies in fully consulting each other's interests.
Indeed, it was less than a year ago that even a document no more formal than a memo of understanding on strategic cooperation fell victim to Israel's annexation of the Golan Heights. This move was not in the spirit of regard for each other's broad policy concerns, said the US in suspending implementation of the memorandum. Prime Minister Begin reacted with the words: ''The people of Israel have lived 3,700 years without a memorandum of understanding with America and will continue to live without it another 3,700 years.'' Despite later moderating exchanges, can such a statement be imagined from any US ''ally'' in the usual sense?
This is not in any way to alter the legitimate ties between Israel and America. But unless an alliance is cemented contrary to the Begin attitude it would be well for Mr. Reagan to keep the true relationship in mind, whether in public or private diplomacy.