Reports citing the emergency services say at least eight people were killed in the fire-ravaged high-rise.
Russian media reports that one man jumped and another fell to his death from the eight-storey block, while Shot media reported that as many as four had jumped from high windows.
One of the men who fell had already suffered horrific burns. The fate of the others was not immediately clear.
Explosions were heard inside the burning block as 100 firefighters battled to rescue people trapped within the building, which is in Fryazino, near Moscow.
The building is thought to house the Platan Research Institute - which develops radio-electronic systems used by Russia's Defence Ministry to jam signals, Newsweek reports.