"According to a recent update, four militants have been killed," the source said. "The last member of the criminal group was found injured in a shed near the house where the other militants were hiding. He died on the way to hospital."
The operation was completed by 18:00 Moscow time (15:00 GMT).
"No civilian casualties have been reported. Two Interior Ministry officers were slightly injured," the FSB said in a statement.
The antiterrorism operation was conducted in Leninkent, some 10 kilometers (6 miles) from the republic's capital of Makhachkala, in an effort to trace gunmen believed to be involved in terrorist attacks and attempts to kill Russian security officers.
Interior Ministry and FSB forces converged on the village around 6 a.m. (03:00 GMT) and by about 8:30 a.m. they had surrounded two private houses near a school. A militant threw a grenade, injuring one police officer, before being shot dead. Two other members of the group later opened gunfire, injuring another officer, and were killed when police returned fire.
Police later said they had identified all of the militants. One of the dead was Omar Sheikhulayev, known as the "Emir of Daghestan." Sheikhulayev, who was on an international wanted list, is believed to have been among terrorists who seized a school in the North Caucasus town of Beslan in 2004. The attack led to the deaths of 331 people, including 186 children.
The other three members of the group were also on the federal wanted list for attacks on police in Makhachkala.
"Sheikhulayev and his group are responsible for a number of serious crimes - in the past three months alone the group has killed five Interior Ministry officers, including the deputy head of the North Caucasus Military District, Maj. Gen [Valery] Lipinsky ", FSB said.
Lipinsky was fatally injured in an attack on his car in Makhachkala in late December.
