"Three militants have been killed in a special operation near the village of Magaramkent in southern Daghestan," the source said. "The so-called 'emir of Daghestan,' Ilgar Malachiyev, was among the dead."
Malachiyev had been stopped in his car by federal troops and was killed when they returned fire.
The source refused to give any further details, saying the operation was ongoing.
According to Daghestan's Interior Ministry, Malachiyev's militant group has some 40 members, three of whom are on the federal wanted list. In 2008, they are believed to have killed five people, including three policemen, and injured nine.
Azerbaijan's National Security Ministry and Prosecutor General's Office earlier said that Malachiyev and his accomplice Samir Makhdiyev were responsible for the August 17 blast in the country's largest Sunni mosque, Abu-Bekr, which left three people dead and 11 injured.