"On the Donetsk direction, the fiercest fighting has been continuing in the city of Artyomovsk," the ministry said in a daily statement, referring to the settlement by its Soviet-era name, Reuters reported.
"Wagner assault units successfully advanced, capturing two areas on the northern and southern outskirts of the city," it said.
The statement said Russian army paratroop units were supporting the claimed advance by holding back Ukrainian forces on the flanks.
Wagner has spearheaded Russia's attempt to take Bakhmut since last summer in what has been the longest and deadliest battle of the war for both sides.
Britain claimed in an intelligence update on Friday that Ukrainian troops had been forced to cede some territory in Bakhmut as Russia mounted a renewed attack there, with intense artillery fire over the previous two days.
MNA/PR