The source did not make clear when Grossi would arrive at the plant. Russian state-owned news agency RIA said the visit had been expected to take place on Wednesday but that it had been delayed by a day.
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Grossi, the head of the International Atomic Energy Agency (IAEA), held talks with Ukrainian President Volodymyr Zelenskyy in Kyiv on Tuesday.
The IAEA said on Sunday it needed access to a site near the Zaporizhzhia plant to check water levels after the nearby reservoir lost much of its water because of the destruction of the Kakhovka dam downstream.
Both sides have accused each other of sabotaging the dam, leading to catastrophic flooding. Western countries say they are still gathering evidence but believe Ukraine would have had no reason to inflict such a disaster on itself.
Russian forces captured the hydroelectric dam and the nuclear plant in southern Ukraine shortly after their February 2022 invasion.
The Zaporizhzhia nuclear plant uses a cooling pond to keep its six reactors from potentially disastrous overheating.
Speaking to reporters in Kyiv, Grossi said there was no immediate danger but that it was a “serious situation.” He said his visit to the facility, Europe’s largest, would provide a more accurate assessment of the risk.
The Kakhovka reservoir was normally used to refill the pond but cannot do so now because of its falling water level, Ukrainian nuclear authorities have said.
Instead, the pond, which is separated from the reservoir, can be replenished using deep underground wells, they said.