"Amir Khairulla, so-called commander of the Eastern Front, who was involved in a series of crimes and terrorist acts in the republic, has been eliminated in a special operation," a ministry source said.
He said Khairulla had been a close associate of Shamil Basayev, Chechnya's number one terrorist, killed in July 2006.
In March 2007, Chechen warlord Doku Umarov appointed Imurzayev "deputy prime minister of Ichkeria" (the name militants use for Chechnya).
The source said the Federal Security Service and the Interior Ministry conducted a joint operation at about 6 a.m. [2 a.m. GMT].
Chechnya's Interior Minister Ruslan Alkhanov confirmed the report.
He said another militant was killed in a separate operation in Chechnya's Grozny area, adding his identify had yet to be established.