Ukraine's army chief Valeriy Zaluzhnyi said Kyiv could not yet confirm whether Russia was indeed pulling out, but that Ukrainian troops had advanced 7km in the past 24 hours and recaptured 12 settlements.

"We continue to conduct the offensive operation in line with our plan," he wrote in a post on Telegram.

A small group of Ukrainian soldiers was shown on Ukraine's state TV in the centre of the village of Snihurivka around 55km north of Kherson city.

They were greeted by dozens of residents in a square, with a Ukrainian flag fluttering from a pole behind them.

"Today, on November 10, 2022, Snihurivka was liberated by the forces of the 131st Separate Intelligence Battalion. Glory to Ukraine!" a commander declared as the locals applauded.

Moscow ordered its troops on Wednesday to withdraw from the entire Russian-held pocket on the west bank of the Dnipro River, including Kherson city, the only regional capital Russia had captured in nine months of war.

Ukrainian officials have so far mostly been wary in public, warning that Russians may still be planning to sow destruction on their way out.

Mykhail Podolyak, an adviser to President Volodymyr Zelenskiy, said on Thursday Russia wanted to turn Kherson into a "city of death", mining everything from apartments to sewers and planning to shell the city from the other side of the river.

"This is what (the) 'Russian world' looks like: came, robbed, celebrated, killed 'witnesses', left ruins and left," he wrote on Twitter.

Russia has been evacuating thousands of civilians from the Kherson area in recent weeks in what Ukraine calls a forced deportation.

Zelenskiy said Ukrainian forces were strengthening their positions "step by step" in the south. "The enemy will make no gifts to us."

Kyiv had hoped to trap thousands of Russian troops in the pocket, and appears to be advancing cautiously to protect its own troops, while inflicting as much damage as possible on the Russians as they try to escape across the river.

Russian state media and pro-Kremlin war hawks defended the retreat as a necessary move while acknowledging a heavy blow.

"I know for sure that this decision was not easy for anyone. Not for those who took it, nor for those of us who understood it would be so but still prayed it wouldn't happen," said Margarita Simonyan, head of RT, Russia's international propaganda channel.

Defence Minister Sergei Shoigu was shown on TV on Wednesday giving the retreat order in response to advice from his top commander who said it was necessary to save the lives of troops who would be better able to defend the Dnipro's opposite bank.

US President Joe Biden said the withdrawal showed there were "some real problems with the Russian military."

Russian forces are still holding on to other gains in the south, including a vital land route connecting Russia to the Crimea peninsula it seized in 2014, and cities in the east that they mostly obliterated while capturing them.

For Ukraine, which has endured nine months of bombardment and occupation that has killed thousands of its civilians, victory in Kherson would strengthen the case that it can defeat Russia on the battlefield, and may quiet some Western voices calling for it to negotiate a deal that would cede territory.

"This is a validation of Ukraine's military strategy and the approach taken by its senior leadership. They are succeeding and the Russians know it," tweeted Mick Ryan, a retired Australian general.

"Now is NOT the time to force Ukraine into negotiations. The Russians might be weakened but they are not giving up on their territorial aspirations. They will have to be beaten on the battlefield and pushed out of Ukraine."

Australian Associated Press