Russia's Defense Ministry claimed that its forces thwarted an attempt by the Ukrainian military to break through its line of control in Kherson, where pro-Russian authorities called on civilians to leave "immediately" earlier on Saturday.
"Due to the tense situation on the front, the increased danger of mass shelling of the city and the threat of terrorist attacks, all civilians must immediately leave the city and cross to the left bank of the Dnieper river," the region's pro-Russian authorities said on social media.
"All attacks were repulsed, the enemy was pushed back to their initial positions," the Defense Ministry said, adding that Ukraine's offensive was launched toward the settlements of Piatykhatky, Suhanove, Sablukivka and Bezvodne, on the west side of the Dnipro river.
The ministry's statement said Russian forces had also repelled attacks in the eastern regions of Luhansk and Donetsk.
Reuters could not independently verify battlefield reports.
Russia is under pressure in Kherson as it braces for a Ukrainian push to retake the region.
Ukraine said on Friday that Russian forces had begun actively moving units and equipment from the west to the east bank of the Dnipro river.
Kyiv has imposed an information blackout from the Kherson front, but Russian commander Gen. Sergei Surovikin said this week the situation in Kherson was "already difficult" and Russia was "not ruling out difficult decisions" there.