Bortnikov said the gang "put on stiff armed resistance and were destroyed" but did not reveal when or where the killings happened.
He said investigators had established the identity of all members of the gang, including the masterminds.
"Today there is an active search for the other members of the group. We know who they are," Bortnikov said.
Medvedev replied: "Identify those involved in committing this heinous crime. Destroy the ones trying to resist. Show no mercy!"
Earlier on Thursday, an attack in Dagestan left at least five people dead.
A bomb and gunfire struck a police-escorted vehicle carrying repair workers on their way to fix a communications tower in the Sergokalinsk region on Thursday, about 80km south of Makhachkala, Dagestan's capital, officials said.
"At around 10.30am [0630 GMT], an explosive device went off as repair workers drove by in a vehicle," a statement released by the investigative committee of Russian prosecutors said.
Five workers were killed and three police injured when one of the vehicles was blown up and in the ensuing gunfire, Vyacheslav Gasanov, a regional police spokesman said.
Gasanov had earlier said eight repairmen had been killed.
An interior ministry spokesman said that police were exchanging gunfire with the attackers hours later.
The communications tower had been blown up the night before by unknown assailants.
Criminal gangs, clan violence and fighters opposing the pro-Kremlin regional government cause frequent battles in Dagestan leading to the deaths of scores of civilians.
Islamic groups in the North Caucasus want a separate state.
Dagestan and neighbouring Chechnya and Ingushetia have suffered increased violence during the past few years, a decade after the second of two devastating wars in Chechnya in which Russian forces drove separatists from power.
A leader of one of the main Chechen groups opposing the regional government claimed responsibility for two bomb blasts in Moscow's metro in March that killed 40 people.
Two days later suicide bombers killed 12 people, mostly police officers, in Dagestan.