Ukrainian President Volodymyr Zelenskiy mocked previous Wagner claims to have seized part of Soledar but made no immediate comment on the latest assertions.
In a statement on Facebook, the Ukrainian military general staff said Russian forces were suffering heavy losses as they tried to take Soledar and sever Ukrainian supply lines.
[1/21] A satellite view shows a smoldering building, in Soledar, Ukraine, January 3, 2023.
One prominent military blogger who posts on the Telegram messaging app under the name of Rybar said Surovikin was being made the fall guy for recent Russian military debacles.
Wagner separately said its forces found the body of one of two British voluntary aid workers reported missing in eastern Ukraine.