Federal Security Service spokesman Alexander Zdanovich said Maskhadov had Deniyev killed under pressure from the rebel warlord Khattab, who goes by only one name.
The Russian Government has accused Khattab of links with Osama Bin Laden's group but the commander said he had not seen him since his years in Afghanistan.
Mr Maskhadov has distanced himself from his two main radical commanders, Shamil Basayev, and the Jordanian-born Khattab, as well as from Ruslan Gelayev, responsible for a recent raid south of Chechnya's border, in Georgia.