(Reuters) -The head of&nbsp;Russia's&nbsp;Wagner&nbsp;mercenary group on Tuesday said his&nbsp;forces&nbsp;controlled more than 80% of the devastated eastern Ukrainian city of&nbsp;Bakhmut&nbsp;after some of war's heaviest and bloodiest fighting.
Senior Ukrainian military officials did not address the&nbsp;claims&nbsp;directly, but said their&nbsp;forces&nbsp;were&nbsp;holding&nbsp;firm&nbsp;against fierce attacks in what once was a city of 70,000 and keeping Russian&nbsp;forces&nbsp;in check.
Wagner&nbsp;fighters have led&nbsp;Russia's&nbsp;months-long efforts to capture&nbsp;Bakhmut. The grinding trench warfare and constant artillery barrages have drawn comparisons with World War One because of massive casualties inflicted on both sides.
Wagner&nbsp;head Yevgeny Prigozhin said his&nbsp;forces, who have played a major role in Russian advances in the east, were pressing on with their encirclement of&nbsp;Bakhmut.
"In&nbsp;Bakhmut, the larger part, more than 80% is now under our control, including the whole administrative centre, factories, warehouses, the administration of the city," he said in a video posted by a Russian military blogger.
The Russian-installed head of Donetsk region, one of four areas declared annexed by Moscow last September, said Russian&nbsp;forces&nbsp;had backed Ukrainian defenders into a corner.
"In the western areas where their units are dug in, they have no choice other than coming forward and giving themselves up," Russian news agencies quoted Denis Pushilin as telling state television.
Serhiy Cherevatyi, a spokesman for Ukraine's Eastern Military Command, said the situation in&nbsp;Bakhmut&nbsp;was under control, adding&nbsp;Kyiv&nbsp;would not allow its troops to be encircled.
Deputy Ukrainian Defence Minister Hanna Malyar acknowledged that&nbsp;Bakhmut&nbsp;"took the main hit" in fighting. But Russian&nbsp;forces, she said, "are generally losing to us in street battles so they are simply destroying all buildings and structures".
Kyiv&nbsp;says&nbsp;it needs more and better Western weapons to beat Russia, and senior Ukrainian officials pressed ahead with their bid to persuade allies to open up stockpiles.
"IRONCLAD" U.S. SUPPORT
Ukrainian Foreign Minister Dmytro Kuleba on Tuesday tweeted that he had received assurances of "ironclad" U.S. support from Secretary of State Antony Blinken.
And Canadian Prime Minister Justin Trudeau, hosting his Ukrainian opposite number on Tuesday, pledged fresh supplies of assault rifles, machine guns and ammunition.
Prigozhin has previously made&nbsp;claims&nbsp;about Russian control of the mining city that turned out to be premature, but Ukraine acknowledges the situation in what it calls "fortress&nbsp;Bakhmut" is now very difficult.
Russia&nbsp;says&nbsp;the capture of&nbsp;Bakhmut&nbsp;will open up the possibility for future offensives across Ukraine, while&nbsp;Kyiv&nbsp;and the West say the now smashed city has only symbolic importance.
Ukrainian President Volodymyr Zelenskiy has vowed to keep defending&nbsp;Bakhmut, but last week acknowledged troops could be pulled back if they were in danger of being encircled.
Russian&nbsp;forces&nbsp;have made only incremental gains in their advance through eastern Ukraine.&nbsp;Kyiv&nbsp;says&nbsp;opposing&nbsp;forces&nbsp;have sustained heavy losses after launching a mobilisation of some 300,000 men late last year.
The lower house of the Russian parliament on Tuesday moved to close loopholes in the draft by introducing electronic military draft papers for the first time in its history. Government officials said there were no plans to compel more men to fight in Ukraine.
(Writing by Gareth Jones, David Ljunggren and Ron Popeski; Editing by Mark Heinrich and Jamie Freed)

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Russia's Wagner claims it controls most of Bakhmut; Kyiv says forces holding firm