By Nick Starkov and Ronald Popeski

KYIV (Reuters) -   Fighting around the eastern Ukrainian city of Bakhmut remained "particularly hot", President Volodymyr Zelenskiy said, giving no indication the city had finally fallen to Russia as claimed by the founder of the Wagner mercenary force.

Yevgeny Prigozhin said his troops, involved in a months-long effort to encircle and capture the bombed-out city, had raised a Russian flag on its administrative building.

"From a legal point of view, Bakhmut has been taken. The enemy is concentrated in the western parts," Prigozhin said in video posted on his press service's Telegram account on Sunday.

But there was no indication from Ukrainian officials that Bakhmut, a town of 70,000 before the Russian invasion launched over a year ago, had fallen into Russian hands.   

Prigozhin has previously made claims that were premature.

Ukraine's military said in a Monday update Bakhmut and several other towns including Avdiivka were at the "epicentre of hostilities".

"The enemy continues its assault on the city of Bakhmut. However, our defenders courageously hold the city," the military said.

Zelenskiy, in his Sunday night video address, thanked soldiers fighting in Avdiivka, Maryinka, and Bakhmut.

"Especially Bakhmut. It is especially hot there," he said.

Ukrainian Deputy Defence Minister Hanna Maliar had earlier described the Bakhmut situation as "tense". Ukrainian forces were defending their positions and Russian forces were paying scant attention to losses as they attacked, Maliar said.

Reuters could not verify the battlefield reports.

CLASHES IN CITY CENTRE

Ukrainian military commanders have said their own counteroffensive - backed by newly delivered Western tanks and other hardware - is not far off, but have stressed the importance of holding Bakhmut in the meantime.

Ukrainian military analyst Oleh Zhdanov said fighting had engulfed the centre of Bakhmut. Ukrainian forces had repelled 25 enemy attacks, but Russian forces had captured the AZOM metal plant.

"The enemy is attacking the city centre from the north, the east and the south and is trying to take the city under its full control," Zhdanov, who has close ties to the Ukrainian military, said in a video on YouTube.

In Russia, a well-known military blogger, Vladlen Tatarsky, was killed by a bomb in a St Petersburg cafe on Sunday in what appeared to be the second assassination on Russian soil of a figure closely associated with the war in Ukraine. 

Russia's state Investigative Committee said it had opened a murder investigation into the blast, which wounded 32 people.

It was not immediately known who was behind the killing. Wagner's Prigozhin said he would "not blame the Kyiv regime" for it but another leading Russian official pointed the finger at Ukraine, without providing evidence. 

A Ukrainian presidential adviser said "domestic terrorism" was breaking out in Russia.