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There was no immediate comment from the Russian authorities.
Though Russian soldiers seized control of Chernobyl soon after the February 24 invasion, the plant's Ukrainian staff continued to oversee the safe storage of spent nuclear fuel and supervise the concrete-encased remains of the reactor that exploded in 1986 in the world's worst nuclear accident.
“According to the staff of the Chernobyl nuclear power plant, there are now no outsiders on site,” state-owned Energoatom said in an online post.
Energoatom had earlier said most troops had gone, leaving only a small number behind.
Russian forces have also retreated from the nearby town of Slavutych, where those who work at Chernobyl live, the company said.
In a separate post, Energoatom said the Russian side had formally agreed to hand back to Ukraine the responsibility of protecting Chernobyl.
It shared a scanned document signed by people it identified as senior staff members at Chernobyl and the Russian military official assigned to guarding Chernobyl.
Reuters could not immediately verify the authenticity of the document.
Ukraine has repeatedly expressed safety concerns about Chernobyl and demanded the withdrawal of Russian troops, whose presence prevented the rotation of personnel for a time.
Earlier this week, workers at the site told Reuters that Russian soldiers had driven without radiation protection through the Red Forest, the most radioactively contaminated part of the zone around Chernobyl, kicking up clouds of radioactive dust.
Asked to comment on the accounts from Chernobyl staff, Russia's Ministry of Defence did not respond.
Energoatom said that as a result of their concerns about radiation, “almost a riot began to brew among the soldiers”, suggesting this was the reason for their unexpected departure.
The IAEA said it had not been able to confirm the reports of Russian forces receiving high radiation doses.
Earlier on Thursday, the head of Energoatom urged the IAEA to help ensure Russian nuclear officials do not interfere in the operation of Chernobyl and the Zaporizhzhia nuclear power plant, Europe's largest, which is also occupied by Russian soldiers.