This week's flareup in communal fighting in Beirut has increased concern here and in Rome about the future of the peace-keeping mission being carried out by the multinational force there. French and Italian leaders have insisted that their own troops should maintain strict neutrality and not be dragged into the fighting between rival Lebanese factions.

There was no immediate reaction to the U.S. announcement that 2,000 more Marines will be sent to the Mediterranean as an offshore backup for the 1,200 already in Lebanon.

However, France also announced that it is sending an aircraft carrier, the Foch, to Lebanon to show the flag and help protect the French contingent.

It is still unclear how West European countries will react to a likely Lebanese government request for an increase in the size of the multinational force later this month, following the expected Israeli withdrawal from the Chouf mountains south of Beirut. The Europeans are seeking to avoid such a painful decision by stepping up diplomatic efforts to bring about national reconciliation in Lebanon.

Addressing a Cabinet meeting here yesterday, President Francois Mitterrand was reported to have said that France did not intend to get caught up in "the mesh of a civil war in Lebanon." A government spokesman later explained that the role of the 2,000-man French contingent was to act as a buffer force between foreign armies and not to side with any of the warring Lebanese parties.

In private, French officials have been critical of the U.S. Marines, who fired on positions of Moslem militiamen earlier this week after themselves coming under rocket fire. The French view is that while such a reaction was understandable, it identified the United States too closely with the interests of the Lebanese Christian Phalangists.

In an attempt to keep an image of strict neutrality, the French contingent refrained from direct retaliation despite the killing of five French military men and the shelling of the French Embassy in Beirut this week. Explaining the restraint, Foreign Minister Claude Cheysson said that there was nothing to prove that the incidents were deliberate.

The deaths of the four French personnel Tuesday seemed to have less impact in France than the killings of the two U.S. marines a day earlier was reported to produce on American public opinion. But Mitterrand's room for maneuver is limited by the commitment of French forces in Chad and the public uneasiness of the Communist Party, which serves as a junior partner in his Socialist-led coalition.

There are domestic constraints of a different kind in Italy, where the government is obliged to consult parliament for any significant changes in the deployment of its peace-keeping contingent. Spokesmen for the powerful Italian Communist Party have demanded a parliamentary debate following rumors that the Italian contingent could be augmented or redeployed in the Chouf mountains.

Italian government ministers attempted to quash the rumors last week following a meeting with President Reagan's Middle East envoy, Robert C. McFarlane, who also visited Paris and London. Defense Minister Giovanni Spadolini told reporters that no increase in the size of the force was envisaged.

Italy's newly appointed Socialist prime minister, Bettino Craxi, sent a personal message to Lebanese President Amin Gemayel yesterday expressing concern at the "intolerable risks" to which the Italy's 2,000-man contingent were being subjected.

The French government, meanwhile, has been attempting to encourage a dialogue between the warring factions. It sponsored a meeting in Paris last weekend among McFarlane, Lebanese Druze leader Walid Jumblatt, and a representative of Christian President Gemayal. In an apparent attempt to pursue this initiative, Mitterrand has dispatched a personal envoy, Francois de Grossouvre, to Beirut.

French forces there, who are responsible for patrolling some of the most dangerous sectors in Moslem west Beirut, are reported to have been reorganized in more defensible positions.

Both French and Italian leaders have made clear, however, that there is no question of pulling their forces out of Lebanon.