UN watchdog 'concerned' about Ukraine nuclear plant access
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They also seized the now-defunct Chernobyl plant right at the beginning of their invasion of Ukraine on February 24, though they have since retreated from there.
International Atomic Energy Agency (IAEA) head Grossi, who has just returned from a trip to Chernobyl, has been in talks with both Ukrainian and Russian authorities to try to ensure safety.
"There is a lot to be done there... we need to go back to Zaporizhzhia. It's extremely important," he said.
He said his agency was still checking on reports that missiles had flown low over Zaporizhzhia, adding this would be "extremely serious" if confirmed.
Grossi said at Chernobyl the IAEA had recorded "an increase in the levels" of radiation during their visit after Russian forces moved with heavy vehicles and dug trenches around the plant.
"But the situation is not one that could be judged as posing a great danger to the environment and to people at the moment we were taking these measures," he added.