The head of the press service of the Daghestani Interior Ministry Abdulmanap Musayev told ITAR-TASS news agency that security forces are looking for "both alive and killed militants."
The Interior Ministry said eight gunmen were spotted on a mountain slope near the Gimry settlement on 3 January.
Russian forces have been pounding suspected militants' positions in the mountains with helicopter gun ships and heavy artillery.
According to the officials, one serviceman was killed and six wounded in the fighting. Russian media say five militants were believed killed so far.
(ITAR-TASS)