Ukraine pushed back Russian forces around Kyiv on Friday, retaking control of some areas near the capital amid fierce battles, Ukrainian officials said.

Russia said during negotiations on Tuesday that it would scale down operations in the Kyiv and Chernihiv regions, both of which are in northern Ukraine, but officials in both regions say fighting has continued in some areas.

"Our troops are chasing them both to the northwest and northeast (of Kyiv), pushing the enemy away from Kyiv," said Oleksiy Arestovych, a political adviser to President Volodymyr Zelenskiy.

He said Russia was also carrying out a partial troop rotation and sending some of its forces to fight in eastern Ukraine.

Ukraine talks to resume, Europe faces Russia gas deadline

Later, local officials said the northern Kyiv region towns of Bucha and Ivankiv had been retaken by Ukrainian forces and Ukraine's armed forces said the nearby town of Borodyanka had also been liberated, sharing a photo of Ukrainian troops they said was taken in the town.

"March 31 will go down in the history of our town... as the day of its liberation from Russian (forces)," Bucha Mayor Anatolii Fedoruk said in a video which appeared to be filmed outside the town hall.

Reuters was unable to verify immediately the information about recaptured settlements, military movements or fighting in the region.

'Risk of dying is high'

NATO Secretary-General Jens Stoltenberg has said Russian forces are not withdrawing but regrouping, while Ukrainian officials say Russian troops are losing ground rather than retreating of their own accord.

But Mayor Vitaliy Klitschko urged residents not to head back to Kyiv yet because "huge" battles were being fought to the north and east of the capital. He did not indicate that these were new battles.

"The risk of dying is pretty high, and that's why my advice to anyone who wants to come back is: Please, take a little bit more time," he said.

The governor of Chernihiv region, where Russian has also pledged to pull back, said some Russian troops had withdrawn but some remained in his region.

"Air and missile strikes are (still) possible in the region, nobody is ruling this out," Governor Viacheslav Chaus said in a video address.

Ukrainian officials also said the southern port city of Mariupol was still holding out after weeks of bombardment by Russian forces and that fighting continued in eastern Ukraine.