The plane, an IL-76 belonging to the interior ministry, crashed about 1 km from Mirny at the start of a flight to Irkutsk, the investigative committee of the Prosecutor General's Office said in a statement.
Russia has one of the world's worst air safety records, with elderly Soviet-era planes, dated airport facilities, poor plane maintenance and lax standards contributing to a grim crash toll.
Last year, all 88 passengers and crew aboard an Aeroflot Boeing aircraft died when the plane crashed in a ball of fire near the Ural mountains. In 2006, 170 people were killed when a TU-154 plane crashed in Ukraine on a flight to St Petersburg.
An interior ministry press service official told the Russian television channel Vesti the plane rolled to the right immediately after take-off.
"The plane flew no more than 2 km at an altitude of 20-30 metres before crashing near an old mine," he said.
