Russian forces have been pounding the positions of suspected militants in the mountains of Untsukul district with helicopter gunships and heavy artillery.
According to the military, one serviceman was killed and six were wounded in the fighting. Russian media say five militants were believed killed so far.
The head of the local administration, Abdulla Magomedov, spoke to RFE/RL's North Caucasus Service from the village of Gimry and said he believed the operation will conclude on 6 January.
“They say the bodies of the gunmen have not been found,” he said. "So far they have completed operations involving helicopters and large-caliber weapons. They still have to search the area, they have to check everything carefully. They were not able to catch anyone today.”
He added that there were reports the militants are from Gimry. “Some say that these people came from outside, that they used to fight in Chechnya. Maybe some of them are from this area, maybe not, it is unclear."
Daghestan's Interior Minister, Adilgerei Magomedtagirov, said security forces will continue the search tomorrow for several militants believed to be still hiding in the mountains.
Russian media said security forces discovered a militant dugout today where they found religious literature and materials for preparing explosive devices.
(RFE/RL‘s North Caucasus service with local agencies)