"The dead militant, whose identity is being established, was carrying a Makarov pistol with the serial numbers erased," the source said.
On Tuesday morning, three men opened fire on a patrol of police officers and Interior Ministry troops. One of the assailants was killed in the ensuing gunfight but two managed to escape.
Local authorities are conducting a wide-scale search for any militants that might have escaped after the attack on Nalchik, the capital of Kabardino-Balkariya, last week.
"The city is divided into sectors, and the search for any possible remaining militants and their accomplices is under way," she said.
According to official data, 92 militants, 35 officers and nine civilians were killed in the October 13 attack on Nalchik.