In the face of a growing challenge to the government of Amin Gemayel, President Reagan says the US Marines will stay in the region as long as there is any hope of a political solution in Lebanon.
But he has backed away from strong support of the May 17 withdrawal agreement between Lebanon and Israel, which the United States helped negotiate. Syria is demanding an abrogation of that agreement as one condition for withdrawal of its forces from Lebanon.
''We are not a party to (the May 17 agreement) so there is no way we should have a position one way or the other on whether it is abrogated or not,'' he said Wednesday. ''That is up to the parties involved. And, no, it would not change our position that as long as there is a chance for peace there we are going to keep striving.''
In a breakfast meeting with reporters at the White House, the President also made these points:
* He feels more optimistic about the chances for improvement in US-Soviet relations following Tuesday's meeting in Moscow between new Soviet party leader Konstantin Chernenko and Vice-President George Bush.
* Not much can be accomplished from a ''get-acquainted'' summit meeting with the Soviets. It is necessary to have an agreed-upon agenda and also a willingness to ''seriously deal'' with those agenda items.
* The US has gone a long way toward redressing the military imbalance with the Soviet Union. But even with deployment of the MX missile and B-1 bomber the US will not be ''equal'' with the Soviets. But his determined goal is to reach an agreement on nuclear arms reduction.
* New taxes are not the answer to the budget-deficit problem.
* The stock market has dropped not because of concern about the economy and the deficit but because of the transfer from equities into higher-yielding bonds.
The President's answers to questions about the Middle East seemed to reflect the administration's growing frustration over events there and uncertainty about what other course of action to adopt. Mr. Reagan suggested there was no alternative to keeping the Marines offshore near Lebanon and trying to help the Gemayel goverment work out a new political arrangement. He said he did not know what could have been differently by the US over the past 18 months or so.
Asked if he would support a new Lebanese government, given Gemayel's weakness , the President was reluctant to speculate on that possibility. When pressed, however, he said ''yes'' if it would be a government that achieved autonomy and sovereignty over its own soil and if the foreign forces in Lebanon were removed.
How long the Marines would remain off the coast of Lebanon depended on what happened, Mr. Reagan said, but it could be for the full 18-month period that Congress authorized.
''We hope that it won't be that long,'' he commented. ''Things do seem to be moving. Sometimes not exactly the way we would like them, but there is still reason for hope and we are going to stay there as long as there is (hope).''
The President said the administration was studying ways to fulfill the role of the multinational forces while providing them with security. A UN force would be preferable, the President indicated, but such a move would be subject to a Soviet veto. ''This would have a legitimate function for the United Nations and (is) what I have always believed the United Nations was set up to do,'' he said.
Mr. Reagan suggested that the Lebanese army, which the US is trying to build up, is a better fighting force than recent engagements suggest. But he admitted that the army is split and that Muslim elements are ''walking away.''
Acknowledging that solution to the Palestinian problem is basic to peace in the Middle East, the President reiterated his commitment to his Middle East peace initiative of Sept. 1, 1982. That was a subject of his meetings this week with King Hussein of Jordan and Egyptian President Hosni Mubarak. Mr. Reagan said the peace process would develop if moderate Arab states would take the lead in negotiating.
''Remember, we start with a situation in which basically the Arab states have simply said, 'We do not recognize Israel's right to exist as a nation,' and so you had the two armed camps,'' said Mr. Reagan. ''Sadat broke that with the treaty of peace with Egypt. Basically, what we're seeking are more Egypts.''
He also distanced the US from PLO leader Yasser Arafat, saying that President Mubarak ''probably believes more strongly than some of us do that Arafat is the legitimate representative of the Palestinians.''
Questioned about the change of leadership in the Kremlin, the President said it afforded a fresh opportunity for trying to reduce tensions in superpower relations. In the meeting with Vice-President Bush, he said, Mr. Chernenko did not retreat from his basic positions. But he expressed a desire for better relations and for mutual efforts to resolve regional conflicts and avoid a nuclear misstep.
''In other words, his whole tone and his words were such that indicated that he believed that there was an area for us to come to agreement on these things, '' the President said.