Authorities in the Russian region of Dagestan on Monday said an operation against gunmen who attacked churches and synagogues and killed at least 20 people was over.

Dozens more were wounded in the attacks.

"Following the neutralisation of the threats to the lives and health of citizens, it was decided to end the anti-terrorist operation in Dagestan," Russia's National Antiterrorism Committee said.

The gunmen who stormed churches and a synagogue in the predominantly Muslim North Caucasus region on Sunday killed 15 police officers and a priest, authorities said.

The attacks took place in the Dagestan capital Makhachkala and nearby Derbent.

"Over 15 police fell victim to the terrorist act," Dagestan's regional leader Sergei Melikov said in a video posted on Telegram, adding that they "protected civilians...at the cost of their lives".

The initial death toll given was eight police officers and a priest. (AFP)