Prigozhin has issued premature success claims before and Reuters was not able to verify the situation on the ground.
On Tuesday, near Bakhmut, a Ukrainian National Guard chief medic who gave his name as Artem said all roads out of the city were under constant heavy shelling.
“Ambulances and other vehicles come under shelling and for that reason it is very difficult to evacuate people. There are high losses, and among medics in particular,” he said.
Russia was throwing more troops into the battle, NATO Secretary General Jens Stoltenberg said before a meeting of European Union defence ministers in Stockholm.
“They have suffered big losses, but at the same time we cannot rule out that Bakhmut may eventually fall in the coming days,” Stoltenberg said.
This would not necessarily be a turning point in the war, he added, but it showed “we should not underestimate Russia, we must continue to provide support to Ukraine”.
EU defence ministers agreed to speed up the supply of artillery rounds and buy more shells to help Ukraine’s military, which is burning through shells faster than its allies can manufacture them.
Under the plan, EU states would get financial incentives worth 1 billion euros to send more of their artillery rounds to Kyiv, while another 1 billion euros would fund joint procurement of new shells.
Russia, which claims to have annexed nearly 20 per cent of Ukraine’s territory, says that taking Bakhmut would be a step towards seizing the whole of the eastern industrial Donbas region, made up of Donetsk and Luhansk provinces.
Western analysts say Bakhmut has little strategic value, although its capture would be a boost to Russian President Vladimir Putin and his military after a series of setbacks in what they call their “special military operation” in Ukraine.
Kyiv says the losses suffered by Russia there could determine the course of the war, with Ukraine expected to launch a counter-offensive when the weather improves and it receives more Western military aid, including heavy battle tanks.
The months of warfare in the east have been among the deadliest and most destructive since Russia invaded in February 2022, adding Bakhmut’s name to a list of devastated cities such as Mariupol, Sievierodonetsk and Lysychansk.
A Ukrainian military drone showed the scale of destruction in Bakhmut, filming apartment blocks on fire and smoke billowing from residential areas.
Iryna Vereshchuk, a deputy Ukrainian prime minister, said fewer than 4000 civilians – including 38 children – out of a pre-war population of some 70,000 remained in Bakhmut, now largely in ruins after months of bombardment.
“The situation in the city is difficult. The enemy actively storms our positions. However, they don’t have any success and suffer colossal losses,” a Ukrainian border guard said in a video released by the State Border Service.
“The city stands because Bakhmut was, is, and will be Ukraine.”
Avril Haines, the main intelligence adviser to US President Joe Biden, described the fighting in Ukraine as “a grinding, attritional war”.
Speaking as the Senate Intelligence Committee began its annual hearing on threats to US security, she said US intelligence did not foresee the Russian military recovering enough this year to make major territorial gains.
Russia casts its invasion of Ukraine as a response to threats to its security from its neighbour’s ties to the West.
Luhansk Governor Serhiy Haidai said Russia’s strategy in eastern Ukraine was to take the remaining areas of Donetsk and Luhansk that it does not control.
“As for tactics – they understand that they are not able to make any rapid advance, so they have one tactic – they advance where they can. If they see that there is any success somewhere, they throw all the reserves into it,” he told Ukrainian TV.