At least 46 people were taken to hospital with injuries after the Sunday evening attack.
Three days of mourning have been declared in Dagestan, a predominantly Muslim republic in southern Russia which neighbours Chechnya.
The apparently coordinated attacks targeted the cities of Derbent and Makhachkala on the Orthodox festival of Pentecost, with an Orthodox priest among those killed.
He was later identified by the head of the Republic of Dagestan, Sergei Melikov, as Father Nikolai Kotelnikov, who had served in Derbent for more than 40 years.
In a series of attacks on Sunday night, gunmen attacked a church and a synagogue in Derbent, which is home to an ancient Jewish community.
In Dagestan’s largest city, Makhachkala, a church and a police post near a synagogue were attacked.
Footage posted on social media showed people wearing dark clothes shooting at police cars in Makhachkala, before a convoy of emergency service vehicles arrive at the scene.
Dagestan has in the past been the scene of Islamist attacks.
Although the assailants have not been officially identified, Russian media widely reported that among the gunmen were two sons of the head of the Sergokala district, Magomed Omarov, who was detained by police.
However, in a video posted on Telegram, Mr Melikov implied Ukraine had been involved in the attack and that Dagestan was now directly involved in Russia’s war in Ukraine.
“The war is coming to our homes,” Mr Melikov said.
“We understand who is behind the organisation of the terrorist attacks and what goal they pursued,” he said.
On Monday, Mr Melikov said authorities were continuing to hunt for members of “sleeper cells” who had prepared the attacks, including with assistance from abroad.
The head of the Russian State Duma’s international affairs committee, Leonid Slutsky, put forward similar claims, saying that the Dagestan attacks and a missile strike which killed four in Russia-occupied Sevastopol on Sunday “could not be a coincidence”.
“These tragic events, I am sure, were orchestrated from abroad and are aimed at sowing panic and dividing the Russian people,” Mr Slutsky said.
But a leading Russian nationalist in occupied Ukraine, Dmitry Rogozin, warned that if every attack was blamed on “the machinations of Ukraine and Nato, this pink mist will lead us to big problems”.
An attack on the Crocus City Hall venue near Moscow in March which left 147 dead was blamed by Russian authorities on Ukraine and the West, even though the Islamic State group claimed it.
Kremlin spokesman Dmitry Peskov said Russia’s President Vladimir Putin offered his condolences to those who lost loved ones in the attacks on Crimea and Dagestan.
Russian news agencies reported on Monday morning that the counter-terrorism operation launched after the attacks had now come to an end.
Between 2007 and 2017, a jihadist organisation called the Caucasus Emirate, and later the Islamic Emirate of the Caucasus, staged attacks in Dagestan and the neighbouring Russian republics of Chechnya, Ingushetia and Kabardino-Balkaria.
Following the Crocus City Hall attack in Moscow, President Vladimir Putin had insisted that “Russia cannot be the target of terrorist attacks by Islamic fundamentalists” because it “demonstrates a unique example of interfaith harmony and inter-religious and inter-ethnic unity”.
However, three months ago Russia’s domestic security service, the FSB, reported that it had thwarted an IS plot to attack a Moscow synagogue.
