Putin has ordered the evacuation of 1,680 people near the seized Ukrainian power plant in Zaporizhzhia.
The UN nuclear watchdog has warned of a potential severe nuclear accident that might hit Enerhodar, next to Ukraine's largest power plant.
Hospitals started to close, and other utility stores along power and water supply due to the evacuation order.
The International Atomic Energy Agency's director general issued a warning that the situation is "becoming increasingly unpredictable and potentially dangerous."
Ukrainian migrants' movement to the seaside villages with beach access has not been verified yet.
Conflicts near the Zaporizhzhia power plant in Enerhodar pose a serious threat to public safety.
The plant produced about half of the nuclear energy produced by Ukraine's four reactors.
Ukrainian forces had little success attempting to retake the facility as missiles from both sides came perilously near to hitting the station.
Last Monday, Ukrainian President Zelensky demanded that Putin be brought before the Hague tribunal for his "criminal acts."
A counteroffensive from Ukraine is anticipated to end the winter standoff this April.