Federal troops engaged a group of up to seven militants on Wednesday afternoon in a forest in the republic's Kazbekovsky District. Two militants were killed at the scene of the shootout, and one died on his way to hospital.
A search for the other members of the group is underway.
On Thursday, six militants on the federal wanted list gave themselves up at a police station in Daghestan. The extent of their involvement in militant activity has yet to be confirmed.
Daghestan borders the troubled Russian republic of Chechnya, which suffered two devastating separatist wars in the 1990s-early 2000s.