Syrian troops conducted mopping-up operations in the mountains dominating Zahle today as Christian militia leaders sought to negotiate a free-saving exit for their besieged forces in the eastern Lebanese city.

As part of the contracts for and end to the fighting, the Christian militias offered to relinquish control of a section of the highway running north-south along the rich Bekaa Valley, which Syria has said it considers essential for its security. Christian sources, reporting this, also indicated that they are basically in no position to dictate terms to the Syrians, who have struck hard at the militias with heavy artillery.

Less violence was reported today in Beirut and Zahle than at any time since the latest round of hostilities began April 2. The Syrians allowed five Red Cross ambulances to enter Zahle, 30 miles east of Beirut, to evacuate 24 wounded civilians and the bodies of four victims of the fighting.

The negotiations were considered a prelude to higher level political talks between the belligerents that, if all goes well, observers expect will be conducted through Lebanese President Elias Sarkis.

Such direct talks were given a greater chance of achieving the Christian militias' goal of forcing the 22,000 Syrian troops to leave, observers said, than a proposed international force. Practical obstacles -- such as splits in the Lebanese government or a probable Soviet veto in the U.N. Security Council -- made formation of such a force, proposed by France with initial U.S. accord, highly unlikely.

Even bringing in soldiers from other Arab armies to reduce the Syrians' overall influence would require approval from Syria and Arab nations willing to provide troops.