Russian officials had denied any knowledge of an accident in September or October.
In a statement, Mayak denied that its plant was the source of increased level of ruthenium 106. Nuclear reprocessing involves separating the radioactive plutonium and uranium from spent nuclear fuel from nuclear power reactors, according to the Union of Concerned Scientists.
"Probes of radioactive aerosols from monitoring stations Argayash and Novogorny were found to contain radioisotope Ru-106", Russia's Rosgidromet service said, according to the South China Morning Post.
The exact origin of the cloud has not been verified but the most likely source is a Russian nuclear reprocessing plant.
Roshydromet, Russia's meteorological agency, said in a release Tuesday that it had detected high readings of the radioactive isotope ruthenium-106 from September 25 to October 1, at observation stations in the southern part of the southern Urals region, not far from the city of Chelyabinsk.
The data appears to back up a report by the French nuclear safety institute IRSN, which said on November 9 a cloud of radioactive pollution over Europe had indicated some kind of leak had taken place at a nuclear facility either in Russian Federation or Kazakhstan in the last week of September.
Air samples in the town of Argayash in late September-early October, for example, showed levels almost 1,000 times higher than those recorded in the previous months.
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"The concentration levels of ruthenium-106 in the air that have been recorded in Europe and especially in France are of no effect for human health and for the environment", the IRSN said in a statement.
"Roshydromet's data on isotope contamination with ruthenium-106 allow us to conclude that the dose that could have been received by a person is 20 thousand times less than the maximum permissible annual dose and does not pose any danger to human health and life", Rosatom added.
"The measurement of its presence in the amounts reported suggest that any biological effects of exposure to this source are essentially similar to that of the normal, naturally occurring radiation background", he told Reuters.
The Mayak site was the location for the third-most serious nuclear accident ever recorded, known as the Kyshtym disaster, which prompted the evacuations of around 10,000 people in 1957. In 2004, it was discovered that Mayak was dumping radioactive waste into the nearby Techa River.
The pollution from ruthenium-106 occurs when atoms are split in a reactor, and is also used in certain medical treatments.
Nearly 30 years later, the extent of the catastrophic Chernobyl nuclear accident - located in Ukraine - was similarly covered up by Soviet officials who for days did not even acknowledge that the incident happened.
Greenpeace said in a statement on Tuesday that it would ask Russia's prosecutors' office to investigate whether there had been an accident in the area.