The agencies reported exchanges of gunfire in the centre of Makhachkala, a region with a long coastline on the Caspian Sea.
An unofficial channel on the Telegram messaging app, Mash, said police were preparing to storm a building where gunmen were holed up in Derbent, about 75 miles further south.
The gunmen attacked a synagogue and a church in Derbent, home to an ancient Jewish community and a Unesco World Heritage site. The interior ministry was quoted as saying that both the synagogue and church were ablaze.
The head of Dagestan’s regional government vowed stiff punishment for “whichever forces lies behind these disgusting actions”.
In Israel, the Foreign Ministry said the synagogue in Derbent had been burned to the ground and shots had been fired at a second synagogue in Makhachkala. The statement said it was believed there were no worshippers in the synagogue at the time.