Russia has replaced Wagner private military units with regular troops in the outskirts of Bakhmut but the group's fighters remain inside the devastated city, Ukrainian Deputy Defence Minister Hanna Maliar said on Thursday.

Her comments appeared at least partially to confirm an announcement by Wagner founder Yevgeny Prigozhin that his group had started withdrawing its forces from Bakhmut in east Ukraine and handing over its positions to regular Russian troops.

"In Bakhmut's outskirts, the enemy has replaced Wagner units with regular army forces. Inside the city itself Wagner fighters remain," Maliar wrote in comments on the Telegram app.

Prigozhin said in a video that the withdrawal of his units had begun early on Thursday and that a handover of Wagner positions would continue until June 1.

Serhiy Cherevatyi, a spokesperson for Ukraine's eastern military command, said the number of Russian attacks in the area had fallen in the last three days, and that there had been two military engagements in the last 24 hours, though shelling continued.

"We can definitely note a reduction in attacks and possibly this is linked to their regrouping. It is clear that we have inflicted heavy losses and they need this (to regroup)," he said.

Maliar said Russia was also reinforcing its positions on the flanks of Bakhmut and shelling Ukrainian forces to try to stop Ukrainian advances to the north and south of the city.

Prigozhin announced the capture of Bakhmut last week after the longest and bloodiest battle of the war. (Reporting by Pavel Polityuk; writing by Tom Balmforth; editing by Timothy Heritage)