The Russian-installed leader of Ukraine’s southern Kherson region, Vladimir Saldo, has called on civilians to evacuate, citing daily rocket attacks by advancing Ukrainian forces.
He urged them to “save themselves” by going to Russia for “leisure and study”, and asked for Moscow’s help.
The call was later echoed by Russian Deputy Prime Minister Marat Khusnullin in a message on state television.
Ukraine rejects accusations that it targets its own civilians.
Its troops have recently retaken some areas of north-western Kherson, closing in on the regional capital.
“The government took the decision to organise assistance for the departure of residents of the [Kherson] region to other regions of the country,” Mr Khusnullin said.
“We will provide everyone with free accommodation and everything necessary.”
Among other weaponry, Kyiv has been using US-supplied Himars rocket systems to great effect, targeting key Russian-held military targets and threatening to cut off the bulk of the occupying forces on the west bank of the Dnieper river (known as Dnipro in Ukraine).
Kherson is the only regional capital seized by Russian forces since Moscow’s invasion began on 24 February.
Ukraine’s military has been tight-lipped about its troop advances in the key region that borders Crimea – the southern Ukrainian peninsula annexed by Moscow in 2014.
In other major developments on Thursday:
This video can not be played
Watch: Trapped boy rescued after Ukraine shelling
Speaking on Thursday, Mr Saldo said many towns in the region – including the two major cities of Kherson and Nova Kakhovka – were now under daily rocket attacks by Ukrainian troops.
“Such strikes are causing serious damage,” he said, urging residents across the whole region – and especially those on the west bank of the Dnieper river – to evacuate to Russia or Crimea.
And he appealed to the government in Moscow to help with this organising this process.
“Russia is not abandoning its people,” he stressed, using a popular saying.
Earlier this month, President Putin declared the annexation of the Kherson and Zaporizhzhia regions in Ukraine’s south, as well as Donetsk and Luhansk in the east.
Ukraine and its Western allies condemned the move, saying it had no legal power. The Kremlin does not fully control any of the four regions.
On Wednesday, the United Nations General Assembly voted overwhelmingly to condemn the Russian annexation attempt.
The assembly’s resolution was supported by 143 countries, while 35 states – including China and India – abstained.
As well as Russia, four countries rejected the vote, namely Belarus, North Korea, Syria and Nicaragua.
Although symbolic, it was the highest number of votes against Russia since the invasion.