Heavy fighting was reported yesterday in southeastern Usulutan Province, where American-trained troops pressed a campaign against leftist guerrillas.

A Salvadoran military source, who asked anonymity for security reasons, said nine guerrillas had been killed in the fighting. He also said an Army lieutenant had been slain in a guerrilla ambush near El Paisanal, a town 27 miles north of the capital.

About 1,500 soldiers from the Army's Atlacatl and Atonatl regiments, specially trained by the United States in antiguerrilla warfare, launched a pincer operation before dawn Thursday in an attempt at trapping leftist guerrillas near the town of Juacaran.

Military sources estimate there are 1,000 guerrillas in the area. The Usulutan area long has been an insurgent stronghold. One detachment of soldiers was reported advancing on foot from the Litoral Highway near the Pacific Coast while another moved down from another highway about 12 miles north of the town.

The troops, armed with 107 mm field cannon and mortars, set fire to underbrush to flush out the guerrillas. Residents reported automatic weapons fire and gunfire all day long around Juacaran, 15 miles east of Usulutan City, the provincial capital.

The guerrillas surrounded Usulutan, 70 miles southeast of the Salvadoran capital, for five days last week, burning scores of buses and trucks on the outskirts of the city and attacking military targets. The guerrillas withdrew on their own last weekend.