Fifteen militants eliminated in Southern Russia
There are no reported casualties among the police.
Relatives of the militants were asked to persuade them to surrender, but the insurgents retaliated by opening fire.
The operation is the biggest success for security forces in Dagestan over the past month.
Last week, a suicide bomber blew himself up, killing four policemen and wounding more than forty civilians.
He had attempted to break the police cordon in republic's capital, Makhachkala.
Dagestan's neighboring republic of Ingushetia is facing a similar battle with insurgents.
President Yunus-Bek Yevkurov of the republic says counter-terrorist operations are vital for the survival of the southern regions.
“We do not want to brutally murder or punish anyone as a warning to others – we just want to deal with this terrorist disease. Perhaps we do not have written permission from the terrorist patient we are treating, but for now we do not have any other choice,” he said.