"An improvised explosive device was found and disposed of," the source said. "The anti-terrorist operation has not ended, the special operation is continuing."
The operation in the village of Alburikent near the Daghestani capital, Makhachkala, started at 8 a.m. Moscow time (05:00 GMT).
Security services said they were looking for the remnants of the militant group led by Omar Sheikhulayev, known as the "Emir of Daghestan," who was killed by security forces earlier this month.
Sheikhulayev was believed to have been among the terrorists who seized a school in the North Caucasus town of Beslan in 2004 and his Shariat Jamaat group has been involved in numerous attacks on local and federal security forces in the North Caucasus.
The group claimed responsibility for the murder of a senior officer with Russia's Interior Ministry, Maj. Gen Valery Lipinsky, in Makhachkala on December 28.