President Reagan, overriding the misgivings of some key advisers, yesterday supported Israel's demands for withdrawal of Syrian troops from Lebanon and the creation of a demilitarized zone in southern Lebanon to prevent Palestinian guerrillas from attacking the Jewish state.

But the president, who met for 2 1/2 hours with Israeli Prime Minister Menachem Begin, reserved a decision on whether U.S. forces will participate in a peace-keeping force to police the proposed buffer zone after Israel withdraws its troops from Lebanon.

A senior administration official later described the talks between Reagan and Begin as "frank, bordering at times on direct and even blunt."

The official also stressed Reagan's "deep concern that the hostilities in Lebanon be terminated at the earliest possible date, that the withdrawal of Israeli forces be accomplished expeditiously and that above all, in an urgent sense, that humanitarian actions be taken immediately to provide for the welfare of noncombatants involved."

The official's comments underscored that Reagan is upset by the heavy number of casualties and the destruction caused by Israel's two-week-old invasion of Lebanon. Because of the widespread death and suffering in Lebanon, some of Reagan's top national security advisers, most notably Defense Secretary Caspar W. Weinberger, are understood to have advocated reacting to Israel's military actions with coolness and possibly a public rebuke.

However, while the president is understood to share some of their misgivings, yesterday he came down squarely on the side of the soft approach recommended by Secretary of State Alexander M. Haig Jr.

In contrast to Weinberger, who on Sunday publicly criticized Israel, Haig has argued that recriminations would only make Begin more intractable and that the United States should try to use the "reality" of Israel's actions as a springboard for resolving the Lebanon crisis.

According to other sources familiar with the meeting, the president seemed to have been swayed by Begin's forceful account of how Israelis residing near the border with Lebanon had lived in constant fear of terrorist infiltration or shellings from Palestinian artillery and rockets. At one point, these sources said, the president told Begin: "Israel should not have to live as an armed camp."

With Begin standing by his side on the White House lawn following their meeting, Reagan said: "It's clear that we and Israel, both, seek an end to the violence there, and a sovereign, independent Lebanon under the authority of a strong, central government."

The president added: "We agree that Israel must not be subjected to violence from the north, and the United States will continue to work to achieve these goals and to secure withdrawal of all foreign forces from Lebanon."

Begin, who has warned publicly against U.S. efforts to pressure his government over Lebanon, reiterated pledges that Israeli troops will be withdrawn "as soon as possible." He added, though:

" 'As soon as possible' means as soon as arrangements are made that never again will our citizens--men, women and children--be attacked, maimed and killed by armed bands operating from Lebanon, and armed and supported by the Soviet Union and its satellites."

The prime minister also objected to characterizations of Israel's action as an "invasion." He said, "This is a misnomer. Israel did not invade any country. . . . We don't covet even one inch of Lebanese soil."

Later, the senior U.S. official, who briefed reporters on condition that he not be identified, said Begin spent considerable time in the meeting with Reagan emphasizing "the unacceptability of the term 'invasion' " to Israel.

According to the official, Begin argued that Israel, retaliating for the attempted assassination of its ambassador in London, initially confined itself to aerial bombing of military targets within Lebanon and did not send its troops across the border until the Palestinians responded with artillery and rocket fire.

While stressing that some blunt language had been exchanged, the official said the meeting ended with the general agreement of both governments that all foreign troops, Syrian as well as Israeli, must be withdrawn; a buffer zone must be established; the authority of the Lebanese central government over the Palestinians must be reasserted, and, following resolution of the crisis, a new, broadened effort must be made to achieve a comprehensive Mideast peace.

In regard to the peace-keeping force, the official said the United States pressed its view that the task be turned over to a strengthened version of the U.N. force, known as UNIFIL, now in southern Lebanon. Other sources said Begin, who regards the United Nations as hostile to Israel, remained skeptical of UNIFIL, which he described scornfully as "the insecurity force," but promised to consider the matter further.

The senior official said Begin had reiterated Israel's preference for a multinational force that would be outside U.N. control and that would include U.S. troops.

Reagan, the official added, made clear that he was "less than enthusiastic" about American participation because of the opposition such a move would encounter in Congress, but the official added that the president "will make a final decision at the appropriate time in the best interests of the peace and security of the region."

In answering questions, the official sought to skirt the impression that the Lebanon crisis had caused new rifts within the administration, notably between Haig and Weinberger, or that it had damaged U.S.-Israeli relations. In response to repeated queries about whether the administration approves or disaproves of Israel's actions, he said:

"Our first order of business is to get the fighting stopped and not to get into public posturing."

Begin is scheduled to meet with Haig and key members of Congress today before returning home.