Ukrainian President Volodymyr Zelensky said Sunday that Bakhmut was "not occupied" by Moscow, while the head of Russia's Wagner mercenary group insisted his fighters had taken control of the eastern city "to the last centimetre".
Kyiv's military said it was hanging on to a small part of the city and said its troops were advancing on its flanks.
A day earlier, Wagner and Moscow's regular army claimed to have fully captured Bakhmut, with Russian President Vladimir Putin congratulating them on the alleged conquest.
But speaking at the G7 summit in Hiroshima, Zelensky denied Russia's claims.
"Bakhmut is not occupied by Russia today," he said during a press conference.
"I cannot share with you the tactical views of our military. The most difficult thing would be if there was some tactical mistake in Bakhmut and our people were surrounded."
Sitting next to US President Joe Biden, Zelensky suggested it would be a pyrrhic victory for Moscow.
Zelensky compared the "absolute total destruction" in Bakhmut to the devastation in Hiroshima when the United States dropped an atomic bomb on the Japanese city in 1945.
"There is absolutely nothing alive (there)."
The Ukrainian army on Sunday said it retained an "insignificant" part of the city and that soldiers were advancing in from the city's outer limits.
"We continue to advance on the flanks in the suburbs of Bakhmut," said Oleksandr Syrsky, commander of Ukraine's ground forces.
- Wagner claims no Ukrainian soldiers left -
But Yevgeny Prigozhin, the chief of Wagner whose fighters have spearheaded Russia's advance on Bakhmut, insisted there were no Ukrainian troops there.
"There is not a single Ukrainian soldier in Bakhmut as we have stopped taking prisoners," he said in a post on Telegram.
"There are a huge number of corpses of Ukrainian soldiers."
Prigozhin said Zelensky was either not telling the truth or "like many of our own military leaders, simply does not know what is happening on the ground, this is a possibility."
On Saturday, he had announced that his fighters had taken full control of Bakhmut.
Prigozhin said Wagner would hand over control of the city to the Russian army by May 25.
But a spokesperson for Ukraine's Eastern Grouping of Forces, Sergiy Cherevatyj, said Ukrainian troops were conducting counterattacks in the city and its surroundings.
Russian forces "are trying to take the whole city under their control. Our units are holding defense -- several buildings and a number of fortifications in the southwestern part" of Bakhmut, he said on national television.
Fierce clashes occurred in other eastern cities and towns including Mariinka and Avdiivka in the Donetsk region, according to a Ukrainian General Staff report, which said Russians conducted four missile strikes and 45 air strikes Sunday.
"Bakhmut and Mariinka remain at the epicenter of hostilities," the report said. "Battle for the town of Bakhmut continues."
The loss of Bakhmut would be hugely symbolic for the Ukrainians, who had held on for months -- ignoring US advice behind the scenes to focus elsewhere.
But some analysts have said Ukraine has inflicted heavy losses on Russia in Bakhmut and forced it to commit large resources, potentially weakening its defences in other parts of the front line.
The fall of Bakhmut would allow Moscow to bring home a key victory after a series of humiliating defeats.
It would also come before a major counteroffensive that Kyiv has been preparing for months.
Zelensky himself has warned that the city's loss would open the way for Russian troops to capture more of the Donbas region.
- Congratulations from Putin -
The Russian army released a statement several hours after Prigozhin on Saturday.
"The liberation of the city of Artemovsk was completed," it said, using the Soviet-era name of Bakhmut.
The Kremlin later congratulated both Wagner and the Russian army, who have been at increasing loggerheads during Moscow's offensive.
"Vladimir Putin congratulated the assault units of Wagner as well as all servicemen of units of the Russian armed forces who provided them with the necessary support and flank cover, on the completion of the operation to liberate" the city, TASS news agency quoted a Kremlin statement as saying.
The two camps are now awaiting the Ukraine counteroffensive, but Zelensky said recently his army needs more time before launching the assault.