One of the slain insurgents was identified as Gamzat Magomedov, leader of the so-called Tsuntinsky gang, which has been accused of committing a string of killings in the Tsuntinsky region of Dagestan since 2010.
Three police officers were wounded in the firefight, the National Anti-Terrorist Committee said.
Magomedov was the second Dagestan insurgent leader to be killed by police in the past week, Russia's RIA Novosti news agency said.
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