By Nick Starkov and Ronald Popeski
KYIV (Reuters) -Ukrainian President Volodymyr Zelenskiy&nbsp;said&nbsp;on&nbsp;Sunday&nbsp;that the military situation was "particularly hot" around&nbsp;Bakhmut, with no letup in a months-long drive to seize the city, the most protracted battle in the Russian invasion.
The founder of Russia's Wagner mercenary force, Yevgeny&nbsp;Prigozhin,&nbsp;said&nbsp;his&nbsp;troops had raised a Russian flag on the administrative building in the city.
But there was no indication from Ukrainian officials that&nbsp;Bakhmut&nbsp;had fallen into Russian hands.&nbsp;Prigozhin&nbsp;has&nbsp;previously made claims that were premature.
"Thank you to our soldiers who are fighting in Avdiivka, Maryinka, and&nbsp;Bakhmut. Especially&nbsp;Bakhmut," Zelenskiy&nbsp;said&nbsp;in&nbsp;his&nbsp;nightly&nbsp;video&nbsp;address. "It is especially hot there."
Russian forces have for months&nbsp;been&nbsp;trying to encircle and capture&nbsp;Bakhmut, a town of 70,000 before the Russian invasion launched over a year ago.
Prigozhin, in an audio message&nbsp;posted&nbsp;on&nbsp;his&nbsp;press&nbsp;service's&nbsp;Telegram&nbsp;account,&nbsp;said: "From a&nbsp;legal&nbsp;point&nbsp;of&nbsp;view,&nbsp;Bakhmut&nbsp;has&nbsp;been&nbsp;taken. The&nbsp;enemy&nbsp;is&nbsp;concentrated&nbsp;in the&nbsp;western&nbsp;parts."
A senior Ukrainian official had earlier described the situation around the town as "tense," with the military command carefully considering every move.
Deputy Defence Minister Hanna Maliar&nbsp;said&nbsp;Ukrainian forces were continuing to defend their positions, with Russian forces paying scant attention to their losses as they mounted attacks.
"The situation in&nbsp;Bakhmut&nbsp;remains tense," Maliar&nbsp;said&nbsp;on&nbsp;Telegram.
"But every military decision and every step is weighed carefully ... We respond to the prevailing situation appropriately, taking into&nbsp;account&nbsp;all circumstances, tasks and the principle of military feasibility."
Zelenskiy and military commanders agreed last month to maintain the defence of&nbsp;Bakhmut&nbsp;amid public debate over whether it was best to remain or adopt other defensive positions.
CLASHES IN CITY CENTRE
Prominent Ukrainian military analyst Oleh Zhdanov&nbsp;said&nbsp;fighting had engulfed the city centre. Ukrainian forces had repelled 25&nbsp;enemy&nbsp;attacks, but Russian forces had captured the AZOM metal plant, which Ukrainian troops had defended for days.
"The&nbsp;enemy&nbsp;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&nbsp;has&nbsp;close ties to the Ukrainian military,&nbsp;said&nbsp;in a&nbsp;video&nbsp;shown on YouTube.
"In some places, we have&nbsp;been&nbsp;successful and in some places we have even staged counter-attacks. But the&nbsp;enemy&nbsp;on occasion registers some success in&nbsp;view&nbsp;of the number of its forces and the number of its daily attacks."
Another military analyst, Yuri Butusov,&nbsp;said&nbsp;Ukraine was hampered by a lack of defensive planning, particularly near Avdiivka, a second town under attack in Donetsk region.
"We still lack planning in terms of building stationary, well-considered, well-defended defensive positions," Butusov&nbsp;said&nbsp;in a weekend interview&nbsp;with Ukrainian NV Radio.
"This&nbsp;is the nature of the crisis near Avdiivka and in other areas of the front. The&nbsp;enemy&nbsp;is knocking out one position after another. And there is no rear position."
In&nbsp;his&nbsp;video&nbsp;address, Zelenskiy also&nbsp;said&nbsp;that two people had died in a Russian mortar attack near the town of Konotop in the northern region of Sumy.
He noted earlier reports that Russian shelling had killed six people in the city of Kostyantynivka in Donetsk region in eastern Ukraine. Eleven people were injured.
(Writing by Ron Popeski and Lidia KellyEditing by Will Dunham, Josie Kao and Matthew Lewis)

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Ukraine's Zelenskiy: situation 'especially hot' in Bakhmut