Several of those who died were thrown into the sea by the force of the explosion on the platform after rocket fuel ignited during the testing of new technologies, Rosatom said, according to Interfax.
The statement said three other staff members sustained injuries and burns of varying degrees and are receiving treatment at the hospital.
He writes that a satellite image shows a nuclear fuel carrier in waters near a missile test site in Russian Federation, where an explosion and fire broke out.
"The search and rescued operation was taking place as long as the hope to find them alive existed".
The company told Russian media that its engineering and technical team had been working on the "isotope power source" for the propulsion system.
Early reports suggested there were heightened radiation levels near the town of Nyonoksa, where there is a site for testing ballistic missiles carried by Russia's nuclear-powered submarines.
There were no further details of the rocket or fuel type.
Authorities in Severodvink, 47km (29 miles) east of Nyonska said that radiation levels shortly after the blast were higher than normal for about 40 minutes but returned to normal.
The ministry claimed "there were no harmful emissions into the atmosphere, the radiation background is normal".
Russian Federation also closed a bay in the White Sea to civilian traffic for a month, driving speculation that either the water had been contaminated or that a search operation was being launched.
Rosatom's description of the incident could indicate it was testing the nuclear-powered cruise missile Burevestnik mentioned during a speech by Vladimir Putin previous year.
He says the ship's presence may be related to the testing of Russia's latest nuclear-powered cruise missile.
The authorities in Severodvinsk, 30 kilometres from the test site, said on their website on Thursday that automatic radiation detection sensors in the city "recorded a brief rise in radiation levels" around noon that day.