"As a result of the operation, three armed rebels were killed. The operation is complete," Arkady Yedelev, the deputy Russian interior minister told journalists outside the apartment block where the gun battle took place.
"One of the bandits was Shamil Gasanov, who is said to be leading this group and who is involved with killing at least five policemen in the last few months," he said.
Neither Gasanov's death nor his influence within Dagestan's rebel setup could be independently confirmed.
Russian authorities have in the past described ordinary rebels they have killed as leaders, and also claimed many times over the deaths of different genuine leaders.
Security analysts said Gasanov had risen to prominence this year and they believe he was in a group who appeared on an Internet video in October taunting Dagestani officials and police.
Hours-long gun battle
Last November, Russian forces killed five men in a shootout at another town in Dagestan. One of the dead was Abu Havs, who the Russians said was an Arab rebel leader with al Qaeda links.
Television footage on Thursday showed two spotlights illuminating a tenth-floor apartment in a scruffy tower block in Makhachkala, from which a gunman sprayed automatic machine gun fire.
In other footage, heavily armed Russian soldiers checked their weapons, manoeuvred behind vehicles and crouched behind walls.
Russian special forces also raided another suspected rebel hideout on Wednesday evening in Makhachkala and said they found a weapons cache and maps of the local area.