Britain, France and Italy jointly sought this week to pressure the United States and Lebanese President Amin Gemayel's government to grant greater concessions to Lebanon's Moslem majority in an effort to get a cease-fire in the fighting there, diplomatic sources said yesterday.

The three European states, which, with the United States, form the multinational peace-keeping force in Lebanon, also reportedly urged in their presentation, decided at a meeting of their foreign ministers in Brussels Tuesday, that greater efforts be made to deal diplomatically with Syria in the negotiated search for a solution in Lebanon.

The three countries, according to these sources, suggested that moving some of the warships of the states of the multinational force away from the Lebanese coast would be a good signal to Syria that the force was interested in negotiating a cease-fire.

This suggestion and the general thrust of the European countries' demarche was turned down by the United States, diplomatic sources said.

A State Department spokeswoman, asked yesterday about the report, said she was "unable to get into anything happening on diplomatic moves in that area" and could not confirm that the countries had approached the United States on the matter. U.S. sources, however, confirmed the general outline of the Europeans' approach and said the United States had rejected it because it would have gone against what it was trying to accomplish in Lebanon and would have sent "mixed signals" to the rival forces there.

The three European members of the peace-keeping force are known to be concerned about the way in which the multinational troops have been drawn into the fighting in Lebanon.

The effect of their decision, which was prepared in a meeting in Rome Monday and adopted the next day in Brussels, is to align Britain and Italy with France, which has repeatedly cautioned the United States about the dangers of deeper involvement in the Lebanese fighting on the side of Gemayel when his government is under internal attack.

Diplomatic sources said that the intent of the demarche was to stress that the multinational force, and particularly the United States, should make it clear that it would not give Gemayel a completely free hand in conducting the war and the negotiations with the Druze and the Syrians, and to make it clear to Gemayel that the Europeans were not interested in isolating Syria diplomatically.

The sources would not disclose what specific concessions the British, French and Italians felt Gemayel should make in order to speed a cease-fire.

A spokesman for the French Embassy, asked about the Brussels decision yesterday, said only that "in keeping with the present situation in Lebanon," it had addressed the "role of the multinational force and of the European contingent, the urgency of a cease-fire and the contribution that each of the countries as well as the international community could make as regards Lebanon."

The French and British ambassadors presented their government's views to Under Secretary of State for Political Affairs Lawrence S. Eagleburger on Wednesday and the Italian ambassador presented his on Thursday, sources said.

A British Foreign Office spokesman said in London yesterday that the three countries had launched their own bid for a cease-fire in Lebanon, in concert with the United States and Saudi Arabia, The Associated Press reported. The spokesman said that "our intent is to supplement, not to undercut, the efforts already under way."

The Times of London said yesterday that "it is understood that the three European countries were becoming increasingly concerned by the United States' action, which they believe falls outside the mission of the multinational force."

British Prime Minister Margaret Thatcher, speaking to American reporters Friday, warned against involving the multinational force more deeply in the hostilities and said Lebanon would be a chief topic in her talks this week with President Reagan.