Italy and France, the United States' partners as peace-keepers in Lebanon, are pressing the Reagan administration to plan an expansion of the size and role of the international force after agreement is reached on evacuating other foreign troops from the country.

Defense ministers from Rome and Paris visited Washington last week and added their voices to Lebanese President Amin Gemayel's plea that he needs this kind of backing from abroad to establish a stable, unified nation sympathetic to the West, according to Italian and French officials. Not wishing to shoulder the responsibility alone, the Europeans want the United States to participate.

"We consider it of the utmost importance to restore the sovereignty of Lebanon, which would become a new moderate state in the Middle East," Italian Defense Minister Lelio Lagorio told Washington Post editors and reporters at a meeting Thursday. "If this requires an increase in the size and scope of the force, then we say 'yes' very quickly."

Observers suggest that the Europeans moreover want to extend the life of the force because they enjoy playing a prominent role on the international stage. Their presence in Beirut adds to their prestige in the eyes of both foreign and domestic audiences.

Lagorio, who recently visited Lebanon, said that Gemayel told him that the Lebanese regular Army would need at least a year before it is ready to police the country on its own and that it plans to build up eight mechanized brigades for the task. Lebanese officials have suggested that the multinational force should be expanded from the current 4,300 to 15,000 or more, although the Beirut government has not yet formally requested such an increase.

President Reagan shares the Europeans' concern for shoring up the Beirut government, in part because this is necessary to complete the unfinished business of evacuating Israeli troops from the country and thus to focus attention on implementing his Middle East peace plan. U.S. officials recognize that it may be necessary to keep the Marines in Lebanon to ensure stability after Israeli, Syrian and Palestinian forces have left.

But this diplomatic goal conflicts with the Pentagon's growing desire to get the 1,200 U.S. Marines out of Lebanon as quickly as possible. Senior military officers say they fear that the Marines cannot avoid friction with other armed groups in the country, a conviction that was reinforced last week when a Marine reportedly came close to firing at an Israeli soldier who he believed was threatening him.

U.S. officials say that they do not wish to make a commitment on staying in Lebanon until agreement is reached for the Israeli, Syrian and Palestinian withdrawal. Defense Secretary Caspar W. Weinberger, in an interview with the Egyptian newspaper Al Ahram to be published today, expressed the desire that the Marines leave Lebanon shortly afterward.

"The multinational force is designed to give . . . confidence that the withdrawal will be completed as agreed upon, and then the multinational force, I hope, would withdraw and Lebanon will become strong enough to take care of these internal security matters on its own," Weinberger said.

Lebanon is filled with so many foreign troops and independent militias that Gemayel's authority is confined to the western half of Beirut. His need for foreign aid in enforcing his rule will become more urgent as the Israelis, Syrians and Palestinians depart and leave vacuums in large swaths of territory where various militias are likely to take power if no central government or international forces move in.

"It will be a matter then of giving this multinational force a mission a little different than it has been, to leave Beirut to move deeper into the country," French Defense Minister Charles Hernu said in an interview with The Washington Post. "To do that, our contingent would want to act in total solidarity with the Americans and the Italians."

The Lebanese Army, generally confined to its barracks since the 1975-1976 civil war, lacks the experience or authority to police the country on its own. Aware of the importance of creating a neutral armed force in the country, the United States has begun training Lebanese soldiers and providing them with arms.