News agencies quoted local Interior Ministry spokesman Abdul Musayev as saying that a group of Daghestani policemen were fired at by a suspected rebel, whom they were pursuing. One officer was killed and two others reportedly wounded.
The spokesman said that the attacker was later killed in a shoot-out after he had taken refuge in a house.
Speaking to RFE/RL, a resident of Gimry -- who asked to be called Akhmed Abdulayev for fear for his safety -- said that the situation in the town is bad and that people in the village feel very unsafe.
"They [the security forces] don't leave us in peace. Neither our young people, nor the village as a whole. They come any time they please and carry out mopping-up operations. It can happen because of slander or lies or false complaints," Abdulayev said.
Daghestan, a Caspian Sea province, borders Chechnya. Its population of 2.5 million comprises over 30 ethnic groups, who use Russian as their common language.
Violence has increased in recent years in Daghestan. The authorities have been quick to blame the violence on Islamic radicals. Disputes among local ethnic groups and homegrown criminal clans are frequent.
Local resident Abdulayev says that "people feel as if laws are not created to defend citizens in Daghestan and officials and security forces can do whatever they want."
RFE/RL authorities contacted the local authorities regarding the day's events in Gimry, but they were unavailable for comment.
Gimry is the birthplace of Shamil, a legendary 19th century anti-Russian leader.