Ukraine is "almost in full control" of Kherson according to Yuriy Sak, an adviser to Ukraine's defence ministry.
Cheering crowds greeted Ukrainian troops as they arrived in the only regional capital to have been captured by Russian forces since its invasion began in February.
Earlier, Ukrainian flags appeared in Kherson after Russia said it had completed the withdrawal of thousands of troops.
The Kremlin's spokesman meanwhile rejects that losing the key southern city is a humiliation for Russia's President Vladimir Putin.
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