This picture shows Russian infantry mobility vehicles GAZ Tigr destroyed as a result of fight in Kharkiv, located some 50 km from Ukrainian-Russian border, on February 28, 2022. (Photo by AFP)
"The Russian army is setting up checkpoints at the entrances of Kherson," mayor Igor Kolykhayev said on Facebook. "Kherson has been and will stay Ukrainian," he said.
Russian President Vladimir Putin ordered his troops to attack Ukraine last week.
Russian troops have invaded Ukraine from several directions, including from Crimea.
Videos on local media in Kherson showed the Russian army entering the city.
"Today, I am responsible for the life of our city and provide protection in the way that our capabilities allow," Kholykhayev said.
He asked people not to leave their homes outside curfew hours.
"The greatest value this city has is your lives. This is not a fight, this is a war," he said.
Kherson has a population of around 280,000 and lies north of the Crimea peninsula, annexed by Moscow in 2014.
Russia claimed to have besieged the city on Sunday.
The Russian army also says it controls the port city of Berdyansk, which lies north-west of Crimea on the Azov Sea.
Russia has faced fierce resistance in Ukraine in its advance on the country.
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