The Ukrainian military has said it repelled numerous attacks in eastern Donetsk over the last 24 hours.
Russian forces have continued to shell settlements along the front line in Bakhmut as they close in on the fiercely contested city.
The commander of Ukraine’s ground forces, Oleksandr Syrskyi, visited Bakhmut on Friday for briefings with local commanders on how to boost the defence capacity of frontline forces.
Denys Yaroslavskyi, commander of a Ukrainian army unit at Bakhmut, told Espreso TV that parts of some units had been ordered to rotate to more secured positions, describing the situation since the morning as "a slaughterhouse on both sides."
Yevgeny Prigozhin of the Wagner Group earlier this week claimed that his forces had taken control of both Yahidne and the adjacent village of Berhivka although it was denied by the Ukrainian military.
He said the city was now completely surrounded with only one route left for Ukrainian troops.
Units of the private military company Wagner have practically surrounded Bakhmut. Only one route out is left,” he said. “The pincers are closing.”
Victory in Bakhmut, a Donetsk province city with a pre-war population of about 70,000, would give Russia the first major prize of a costly winter offensive after it called up hundreds of thousands of reservists last year.
Drone footage this week showed the destruction inflicted on Bakhmut, with many buildings levelled by the fighting. An estimated 5,000 of a pre-war population of 70,000 are believed to remain in the city.
Bakhmut has been a priority target for the Wagner militia since last autumn, which has focused resources and manpower on the area.
Western analysts claim the group has employed “human wave” attacks reminiscent of First World War tactics in an effort to break down Ukrainian defences. One NATO assessment claimed that Russia is losing up to 2,000 soldiers for every 100 yards gained.
Wagner forces have been strengthened by prisoners, enlisted with the promise of freedom if they survive a six-month term at the front.
Amid the situation in Bakhmut, US officials have urged Ukrainian military chiefs to redirect their focus to preparations for a counter-offensive to liberate Russian-occupied territory.
Volodymyr Zelensky said last week that “it is important for us to defend it, but not at any price”.
“After the liberation of Yahidne, Wagner assault units continue to advance,” reported the Russian Telegram channel Rybar, claiming that the city is almost surrounded. “The only route to the city runs through a country road whose condition does not allow it to be used properly.”
Other thrusts along the front line have faced setbacks. In the mining town of Vuhledar to the south, military channels have reported heavy Russian losses. But the advance is continuing, with forces massing around the small town.