The house in Makhachkala was badly damaged in the fighting
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A day of fighting in parts of Russia's North Caucasus region close to Chechnya has left four suspected militants and three police officers dead.
Security forces in Dagestan killed the suspected militants in a two-hour gun battle after besieging a house in the regional capital, Makhachkala.
A policeman and a woman inside the building were also injured.
In Ingushetia, gunmen killed three policemen and wounded one in an ambush near the North Ossetian border.
Two Russian servicemen were wounded in a roadside bomb attack in Ingushetia late on Friday.
Hand grenade
In Makhachkala, one report said a number of children had been allowed to leave the house - in a residential part of the town - before the fighting began.
Two women were arrested after the battle.
Adilgerey Magomedtagirov, Dagestan's interior minister, told Russian TV that police had received information that the house contained "several armed militants intent on terrorist attacks".
According to Russian TV, an appeal for the occupants to surrender was met with a hand grenade after which police bombarded the building.
Mr Magomedtagirov described two women who left the house as "Wahhabi" - a term commonly used in Russia to describe radical Muslims.