Vladimir Saldo said an estimated 10,000 people a day would be moved over the next six days.
The Russian-installed leader of the annexed Ukrainian region of Kherson said on Wednesday that authorities plan to evacuate around 50-60,000 people over the next six days amid escalating pressure from a Ukrainian counteroffensive.
Speaking on an online broadcast of "Soloviev Live", Russian-intalled governor Vladimir Saldo said authorities were moving civilians to the left bank of the Dnipro in order to "keep people safe" and allow the military to "act resolutely".
"I drove through the regional centre this morning. On the exterior, there was nothing to suggest there was a lot of pressure," Mr Saldo said.
"But when I arrived at the river port I saw that the boats were waiting and are already loaded with people ready to go to the left bank of the Dnipro," he said, adding that the situation "is getting tense."
He said an estimated 10,000 people a day would be moved over the next six days, and that some regions in Russia were being prepared to accept people.
More than 5,000 people have already left Kherson in the last two days, Mr Saldo told state television.
Russian forces in the Kherson region have been driven back by 20-30 km (13-20 miles) in the last few weeks and are at risk of being pinned against the western bank of the 2,200-km-long Dnipro river that traverses through Ukraine.
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