Ukraine on Friday announced that its forces were entering the city of Kherson, hailing an "important victory" after Russia said its troops had retreated from the only regional capital it had captured in nearly nine months of fighting.

Ukraine's parliament published pictures of people carrying Ukrainian flags in the centre of Kherson, the capital of the eponymous region and close to the Black Sea.

Hours earlier, Russian strikes killed seven people in Mykolaiv, a nearby city in southern Ukraine on the Black Sea that the Russians have failed to capture but subjected to months of attack.

"Kherson is returning to Ukrainian control and units of the Armed Forces of Ukraine are entering the city," Kyiv's defence ministry said on social media.

It added that its artillery teams had clear views over Russia's routes to retreat and warned: "Any attempts to oppose the Armed Forces of Ukraine will be stopped."

Kherson was the first major urban hub to fall after President Vladimir Putin ordered Russian troops into Ukraine on February 24.

Its full recapture by Kyiv would be a political and symbolic blow to Putin and open a gateway for Ukraine's forces to the entire Kherson region, with access to both the Black Sea in the west and Sea of Azov in the east.

"Ukraine is gaining another important victory right now and proves that whatever Russia says or does, Ukraine will win," Foreign Minister Dmytro Kuleba wrote on social media.

He posted an amateur video showing Ukrainians removing a billboard near Kherson that proclaimed: "Russia is here forever".

The Russian defence ministry said earlier: "The transfer of Russian troops to the left [eastern] bank of the Dnipro River was completed. Not a single piece of military equipment and weapons was left on the right (western) bank".

While it would appear a major Russian setback, the Kremlin insisted that Kherson was still part of Russia and that it did not regret annexing the entire Kherson region at a lavish ceremony in late September.

"This is a subject of the Russian Federation. There are no changes in this and there cannot be changes," spokesman Dmitry Peskov told reporters. (AFP)