Residents of Nenoksa, the village closest to the incident, were told to leave on a special train, TV29, reported on Tuesday. It attributed the move to events at the nearby base of 5 a.m. to 7 a.m.
Severodvinsk said in a statement to Interfax that the population of the village had been advised to be out of the area by Wednesday because of unspecified "planned activities" at the military testing range.
"The leadership of the Nenoksa testing range of the Military Authorities," the statement said.
Later in the day, however, a report on Interfax suggested that the evacuation might have been canceled.
The Russian authorities have not linked this to what they say the accident.
Russian statements about the radiation release have been contradictory. Scientists with the Russian Federal Nuclear Agency said the radiation levels had climbed to twice the background level in Severodvinsk, about 25 miles from the test site.