MOSCOW, May 21 (Reuters) - The head of Russia's Wagner mercenary group said on Sunday that his forces had captured all the territory in the eastern Ukrainian city of Bakhmut as promised and would leave the conflict zone later this week.

"Wagner has made no advances. Wagner today captured no territory. We have captured all the territory we promised to capture, right up to the last centimetre," Yevgeny Prigozhin said in an audio message posted on Telegram messaging app.

"As we stated yesterday. We are handing over our positions to (Russia's) Defence Ministry and on the 25th (of May) we are leaving the conflict zone."

Prigozhin said on Saturday that his forces had taken control of Bakhmut, under attack by Russian forces for more than nine months. But Ukrainian President Volodymyr Zelenskiy and military chiefs denied this on Sunday.

Reuters could not verify the battlefield reports.