MANILA — Four Abu Sayyaf militants were killed on Saturday in a gunfight with the police and troops in the central Philippines, more than a week after the group surprised the authorities by venturing north of its traditional stronghold and engaging in deadly clashes, the military said Sunday.

A spokesman for the military said security forces were hunting several other members of the terrorist group on the tourist island of Bohol, in the central Visayas region. They recovered at least three high-powered firearms from the group.

The violent confrontation occurred after an Abu Sayyaf member gave away the group’s location when he went to town to buy bread, the authorities said.

“The hunt continues for the remaining two or three terrorists who were part of the band that attempted to establish a foothold in Bohol but failed,” said Col. Edgard Arevalo, the military spokesman. “We have reports indicating that they were also wounded and running out of supplies.”