NATO Secretary-General Jens Stoltenberg welcomed Russia's withdrawal from the Ukrainian city of Kherson with caution, but said if confirmed, it would be "another victory for Ukraine."

"We have taken note of the Russian announcement to retreat from Kherson," Stoltenberg said. "We have to see how the situation on the ground develops in the coming days."

Speaking alongside the new Italian Prime Minister Giorgia Meloni, the top NATO official stressed that Russia's military campaign following the invasion of Ukraine was struggling.

"What is clear is that Russia is under heavy pressure and if they leave Kherson, it would be another victory for Ukraine," the alliance's secretary general said.

Ukraine said Thursday its forces had reclaimed a dozen villages in the southern Kherson region, a day after Russia ordered its troops to withdraw from the eponymous city.

"We have seen how the Ukrainian armed forces have been able to push back Russian forces and liberate territory," Stoltenberg said.

"These gains belong to the brave courageous soldiers of Ukraine.

"At the same time, the unprecedented support that NATO allies, including Italy, have provided is making a difference on the battlefield every day and remains vital for the Ukrainian progress."

The advance took place less than a day after Moscow ordered its troops 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 the war.

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

An adviser to Ukraine's president 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," Mykhailo Podolyak wrote on Twitter.

Russia denies it abuses civilians despite bombarding residential areas throughout the conflict. It has been evacuating thousands of civilians from the Kherson area in recent weeks in what Ukraine calls a forced deportation.