Russia has withdrawn over 30,000 troops in the southern Kherson region in Ukraine, according to its defense ministry, while Kyiv said its forces were entering the city.

"In total, more than 30,000 Russian servicemen, about 5,000 pieces of hardware and military equipment and materiel have been withdrawn," the defense ministry said. "Not a single piece of military equipment or weaponry was left on the right (western) bank."

It said Russia had not suffered any loss of personnel or equipment during the withdrawal.

The ministry did not comment on Ukrainian officials' assertions that Russian troops in Kherson had been ordered to change into civilian clothes.

It was not possible for Reuters to assess whether or how many Russian troops were still in the city.

Earlier this week, Russian Defense Minister Sergei Shoigu ordered the withdrawal of the troops, marking one of the most significant retreats since the beginning of the war.

Ukraine's defense intelligence agency said on Friday that Ukrainian units were entering the southern city of Kherson and told any Russian troops still there to surrender.

In a statement issued in Russian, the agency said Kherson was coming back under Ukrainian control after being occupied since March and threatened to "destroy" any Russian soldiers who resisted.

"You have only one chance to avoid death - immediately surrender," the Main Intelligence Directorate of the Defence Ministry said in a statement on the Telegram messaging app.

The statement, which offered the first official confirmation that Ukrainian forces were in Kherson, guaranteed the safety of any Russian soldiers who surrendered.

It said that Russian troops still in the city had been ordered by their commanders to change into civilian clothes and to hide.