On Saturday, authorities introduced counter-terrorism emergency powers in the town of Karabulak after the alleged militants had opened fire on law enforcement forces in a residential building.

"The special operation has ended. The counter-terrorism operation regime is still in place," a law enforcement source told TASS.

Identities of the alleged militants were being established, RIA Novosti news agency reported, citing a source.

Ingushetia, the smallest region in Russia, is wedged between North Ossetia and Chechnya. It has a population of about half a million people.

For almost a decade until 2017, Russian security forces were battling an armed insurgency conducted by an array of Islamist militant groups in Ingushetia as well as in Dagestan and Chechnya.

(Reporting by Lidia Kelly in Melbourne, Moscow bureau; Editing by Jamie Freed and Elaine Hardcastle)