At least 15 law enforcement officers and four civilians were killed in two seemingly coordinated attacks by gunmen in Russia’s southern republic of Dagestan, Russian investigators said on Monday.

Wielding rifles and Molotov cocktails, the attackers assaulted synagogues and Orthodox churches on Sunday night in two major cities of Dagestan, a predominantly Muslim region on the Caspian Sea.

One of the civilians killed was Nikolai Kotelnikov, a priest in the city of Derbent. The attackers also set fire to a synagogue in the city.

For hours, the gunmen were on the loose, engaging in shooting sprees with members of the law enforcement, according to statements from the region’s interior ministry. Five attackers were eventually killed, local officials said.

Russian investigators designated the attack an act of terrorism, but it was not immediately clear who was responsible.

Local officials declared a three-day mourning period in Dagestan, a multireligious and ethnically diverse region, and said families of the victims would receive special compensation.

The Kremlin spokesman said on Monday that President Vladimir V. Putin was receiving regular reports on the attack, but that he did not plan to address the nation about it. The spokesman, Dmitri S. Peskov, declined to comment on the gunmen’s motives.

The attack was the latest in a series of acts of extremist violence in Russia in recent months, underlining the country’s complex security challenges as it remains bogged down in a war against neighboring Ukraine.

In March, four gunmen killed 145 people at a concert hall near Moscow in an attack claimed by the Islamic State. And in Dagestan last October, a mob, apparently searching for Jewish passengers, stormed a plane arriving from Tel Aviv.

Russian officials tried to mask intelligence failures surrounding the Moscow concert hall attack by blaming it on the West and Ukraine, without providing evidence. And initial statements by officials after Sunday’s attack suggested that the government may adopt a similar tactic in Dagestan.

“We understand who is behind these acts of terror,” Sergei Melikov, the top official of Dagestan, said in an address to its residents. He made a comparison between the victims of the assault and Russian soldiers fighting in Ukraine, saying they were facing the same enemy.

“We need to understand that war comes into our home,” Mr. Melikov added.

Mr. Peskov, the Kremlin’s spokesman, in his daily news briefing on Monday appeared to draw a connection between the Dagestan violence and a separate attack by Ukraine on Sunday on occupied Crimea. He did not, however, directly blame Ukraine or the West for the attack in Dagestan.

Russia’s antiterrorism committee, a body that coordinates the fight against terrorism in the country, said in a statement that two attackers had been killed in Derbent and three more in Makhachkala. It said that law enforcement officers were looking for accomplices.

The investigators did not disclose their identities, and their motives were not immediately clear.

The agency also posted a video showing burned cars, guns in pools of blood and heavily armed security service officers chasing the apparent perpetrators inside an Orthodox church. The video could not be independently verified.

Mr. Melikov said a manhunt would continue in the republic until “all members of extremist sleeping cells” that were “undoubtedly prepared also from abroad” were caught.

On Monday, he visited the sites of attack in Derbent. He walked through the halls of the local synagogue, home to one of the oldest Jewish communities in Russia. The synagogue’s main hall was burned down as a result of the attack, according to a video posted by the regional government. That video also could not be independently verified.