Russia last month abandoned the west bank - including the city of Kherson - in one of its biggest retreats of the war. That pullout means the vast Dnipro now forms the front line of the war in the south of the country, with both sides exchanging heavy fire from positions on opposite banks.
The Russian-imposed administration in Kakhovka said bedridden or handicapped people would be taken to the Henichesk district to the southeast. "Take care of yourself and those close to you!" it said in a Telegram post, encouraging people to register for the evacuation.
Authorities have set up a hotline to help those leaving.
A woman who answered the hotline phone said a broad evacuation was taking place from a string of settlements on the left (east) bank of the river, including Oleshky and Nova Kakhovka, the site of a huge hydroelectric dam.
"Since Oct. 20, martial law was introduced. All civilians are being evacuated," she said.
She was referring to a martial law announcement by Russian President Vladimir Putin that applied to Kherson and three other partly occupied regions of Ukraine that he has proclaimed part of Russia, in a move condemned as illegal by most countries.
She declined to comment on conditions in the affected towns, the reason for the evacuation or the number of people affected.
Before giving up Kherson, Russia evacuated tens of thousands of its residents in an operation that Ukraine described as a forced deportation.
Kherson authorities are encouraging people to leave parts of the east bank and promising that those who do so will be well looked after elsewhere. In another post on Friday, the Kakhovka Telegram channel published what it said was a message from an unnamed evacuee praising the welcome they had received in the Russian coastal town of Anapa.
"Every day we go for walks by the sea," it said. "We are very happy we came here. They take care of us, help with everything. If anyone is in doubt about whether to go or not - do not hesitate, leave!"
(Reporting by Mark Trevelyan; editing by Frank Jack Daniel)
