Lebanese President Amin Gemayel told President Reagan yesterday that he favored an expanded multinational force that would stay in Lebanon until all foreign troops have left the country, a senior U.S. official said in describing the first meeting between the two leaders.

The official said Reagan told the Lebanese leader during their White House talks that the administration would give the matter careful consideration. Other well-placed administration sources said that Reagan appeared to be open to the idea.

In public statements, Reagan said his talks with Gemayel had focused closely on the "shared objective of prompt withdrawal of all foreign forces from Lebanon," but the suggestion of an expanded multinational force appeared to reflect the difficult road ahead in reaching that goal.

"I'm not discouraged, but it's going to be tough," said the senior U.S. official, who cannot be identified under the ground rules for his remarks.

The official said the Lebanese government faces a "practical numbers problem and a logistical problem. The Lebanese army is still limited in numbers. The Lebanese see how long it will take to double or triple the size of the army and how long it will take to train them and come to the conclusion they need some help."

Gemayel met with Secretary of State George P. Shultz for a working lunch following the morning meetings with Reagan and other top administration officials at the White House.

While the talks were understood to be general in nature, initial discussions appeared to focus on eastern and northern Lebanon as possible new areas for use of the multinational units, but the sensitive southern region also remains a possible area for deployment.

Some 3,400 U.S., French and Italian troops currently are deployed only in part of Beirut.

In later discussions with Secretary of Defense Caspar W. Weinberger, Gemayel received pledges of increased military support from the United States in rebuilding and vastly expanding the Lebanese army.

Most of yesterday's discussions dealt with problems of the future of Lebanon, but Gemayel also gave Reagan's Middle East peace initiative one of the strongest endorsements it has yet received from a regional leader.

"American commitment to the sovereignty and territorial integrity of a free democracy in Lebanon has been fundamental to our survival. We see the U.S. role as the indispensable ingredient to bring peace not only to Lebanon but also to the whole region as well," Gemayel said. "We firmly believe that President Reagan's initiative has created unprecedented opportunities for peace."

After meetings dealing primarily with Lebanon with Israeli Foreign Minister Yitzhak Shamir last week and with Gemayel yesterday, administration attention now shifts to the broader Middle East peace question with the arrival starting today of a group of Arab leaders to outline the positions taken at last month's Fez summit meeting.

Morocco's King Hassan heads the delegation, but the final makeup of the group remains uncertain. Originally the foreign ministers of Saudi Arabia, Syria and Tunisia were to accompany him. That group now may be expanded to include Jordan and Algeria.

While U.S. officials do not rule out progress on the Reagan peace initiative prior to getting foreign forces out of Lebanon, they have said an agreement on withdrawal appears to be necessary before much momentum can be built on the broader question.

The senior administration official who outlined the course of the talks with Gemayel said yesterday that major issues remain unresolved in the talks on the future of foreign forces in Lebanon: an agreed framework for the removal of all the forces, the nature of peace-keeping forces to be deployed in southern Lebanon, an acceptable security arrangement for the south and the issue of the future of the multinational force.

The official said the target date of the end of the year for removal of foreign troops remains "a good one" and that the president has made it clear that he places the highest priority on this issue.

There was no official response yesterday from the Pentagon on the possibility that the multinational force, which now includes 1,200 Marines, be enlarged and its role expanded.

Officials said privately that if Reagan decides that more Marines could help the Lebanese government gain authority, Weinberger would undoubtedly carry out the president's instructions. But it is no secret within the Pentagon that Weinberger has "always been very anxious to restrict the American role and keep it tight," as one official put it.

Gemayel met at the Pentagon yesterday afternoon with Weinberger and other U.S. civilian and military officials.

After that session, the Pentagon issued a statement in which Weinberger said the United States "was prepared to assist the Lebanese armed forces with training, material, logistics and planning support, subject to the necessary congressional approvals."

Weinberger said a U.S. military survey team had just completed a study in Lebanon to see what was needed.

Officials said privately that while the survey team has not yet reported formally, it is expected that assistance will center on helping the Lebanese build a well-armed police force to take care of internal security rather than external threats. They estimated that U.S. military aid initially may involve perhaps two dozen light armored vehicles.

The Lebanese army is central to a major dilemma now facing American negotiators trying to work out the withdrawal from Lebanon of all foreign forces -- Israelis, Syrians and Palestine Liberation Organization troops.

As the price for withdrawal, the Israelis want, among other things, an agreement with Lebanon for a security zone in southern Lebanon that would be patrolled by strong forces able to protect Israel's northern borders. The Lebanese army, U.S. officials acknowledge, cannot fill that role now and how fast it could be made into an effective force is uncertain.

The Israelis favor leaving the Christian militia led by Maj. Saad Haddad, whose forces are supplied and supported by Israel, in any southern Lebanon security zone. That is unacceptable to Washington and Beirut, at least at the moment.

In an effort to try to balance the need of Israel for secure borders with the effort to get the Israelis out of Lebanon as fast as possible along with the Syrians and PLO, the United States is discussing options which could include using the existing United Nations force in southern Lebanon, which is based north of Haddad's forces, perhaps in another location. The Israelis, however, object to the U.N. forces as a border force.

That is why the concept of expanding the current multinational force is also being discussed, although formal U.S. positions still are being formulated. The officials also stress that Israel's positions do not appear "to be set in concrete."