Israel's Prime Minister Menachem Begin has gained support from President Reagan for a major objective: the withdrawal of all foreign forces from Lebanon.
In return, the President was reported to have asked the Israeli leader to continue to restrain his forces from advancing farther into the city of Beirut and to consider new moves aimed at resolving the Palestinian issue.
The new element in all this is a Reagan administration attempt to argue that Israeli successes in Lebanon ought to allow the Israelis to be more forthcoming on the Palestinian question, particularly when it comes to the future of more than 1 million Palestinians living in the Gaza district and on the West Bank of the Jordan River.
Unlike President Reagan's first meeting with Prime Minister Begin last September, when he avoided any substantive discussion of the sensitive Palestinian issue, the President went into a White House meeting with Mr. Begin on June 21 armed with facts and arguments on the subject.
A senior United States official said that the President emphasized the need for an expeditious withdrawal of Israeli forces from Lebanon. At the same time, the President agreed that there was a need to create a buffer zone in southern Lebanon designed to prevent further Palestinian attacks on Israel. According to the US official, the discussion between the two leaders ''bordered at times on being . . . blunt.''
The President's advisers have been divided, meanwhile, over how the US should deal with the Israeli invasion of Lebanon. Until recently, the President favored the more restrained approach advocated by Secretary of State Alexander M. Haig Jr. over the harsher attitude toward Israel favored by Defense Secretary Caspar W. Weinberger. Mr. Weinberger fears that the invasion has severely damaged American credibility among the Arab nations. But White House officials have reported that not just Mr. Weinberger but the President himself was angered when the Israelis seemed to go beyond the objectives that they set at the start of the invasion.
Mr. Begin, for his part, warned several days prior to the meeting with President Reagan that he would not yield to pressure, even if it was friendly pressure from the US.
Disagreement between the two leaders arose over the question of an international peacekeeping force. The US would like to strengthen and expand the United Nations force in Lebanon. But Prime Minister Begin argued that this force has been ineffective in preventing Palestinian infiltration into southern Lebanon. The Israeli leader suggested instead a new international peacekeeping force, which might include US troops.
According to a senior US official, President Reagan was reluctant to agree to such a proposal because it would raise strong objections among Americans. Other sources said that the participation of US troops would also, almost inevitably, provoke the Soviet Union and place American soldiers in ambiguous and dangerous situations.
The two leaders did agree, however, on the desirability of a Syrian withdrawal from Lebanon and the removal of military forces of the Palestine Liberation Organization (PLO) from the Lebanese capital. The deal that both the US and Israel seem to envisage is a reassertion of Lebanese central government control over the parts of West Beirut now held by the PLO in exchange for a withdrawal of the Israeli forces now surrounding Beirut.
In the view of some experts, however, it is doubtful whether the Reagan administration can succeed in linking all this to progress on the issue of autonomy for the Palestinians living on the West Bank and in Gaza. Indeed, the administration has done little in the past to restrain Begin government moves aimed at tightening control over the West Bank and Gaza. Some of the experts think that, given their military victories in Lebanon, the Israelis will simply accelerate those moves.