The United States and its European partners in the multinational force in Lebanon proposed today that the United Nations play a role in supervising the new cease-fire in Lebanon, but their suggestion was being resisted by Syria.

The U.S.-European view was made public following a meeting of Secretary of State George P. Shultz with the foreign ministers of France, Italy and Britain, the other contributors to the multinational peace-keeping force that has been in and around Beirut for about a year.

The cease-fire reached Sunday between the Lebanese government and warring factions is to be policed by "neutral observers," according to the Lebanese government announcement. But there has been no agreement about who these observers will be.

State Department spokesman John Hughes said Shultz and his colleagues agreed in their meeting that if possible the neutral observers should have "an affiliation with the United Nations . . . in some way not yet specific."

Hughes discouraged any speculation that the multinational force, including U.S. Marines, might expand its role and territory to supervise the cease-fire in the mountains near Beirut. U.S. officials said that American troops would not be considered "neutral enough" for such a mission although it is possible that some of the European countries involved in the multinational force might participate.

The British foreign secretary, Sir Geoffrey Howe, said a U.N. affiliation was desirable because of the experience and readily available machinery of the world body. Howe suggested that the cease-fire observers may be needed for a long period of time into the indefinite future, longer than the multinational force "which hopefully has come close to its conclusion."

There was no discussion in the four-power meeting today about withdrawal of the Marines and other parts of the multinational force, according to U.S. sources. Such discussion is considered by Washington to be premature until the situation in Lebanon is stabilized.

The outsiders being sought to supervise the truce would be "observers" who would be lightly armed and not in a position to interpose themselves between rival fighting forces. This would distinguish them from the more heavily armed "peace-keeping force" composed of U.S. Marines and European forces.

U.S. sources said Syria was initially negative about a U.N. role in supervising the truce, although there were some suggestions that this was not a final position and that Syria hopes to use its leverage to pick and choose among the possible participants in an observer force.

The most likely U.N. organization to be involved would be the United Nations Truce Supervision Organization (UNTSO), which was created following the first Arab-Israeli war in 1948. Its complement of about 300 observers includes 50 who are currently stationed in and around Beirut. UNTSO's ranks include 37 Americans and 34 Soviets.

An expansion of UNTSO's personnel and role might not require a full vote of the Security Council but U.N. officials are reported to have concluded that it would require the concurrence of council members. This would be difficult if Syria objects, because the Soviet Union, a permanent member of the council, is expected to support Syria's position.

The Soviet Union is reported to be leaning against a U.N. role in a cease-fire force but has not yet transmitted a clear official position, U.N. sources said.