Moscow: Moscow said on Thursday that Russian forces were "blocking" Ukrainian forces from entering or leaving the frontline hotspot of Bakhmut.
However, the head of the mercenary group Wagner, which has led much of the fighting for the city, said it was "too early" to say Bakhmut was surrounded.
Kyiv has yet to respond to the claims of the longest and bloodiest battle since the start of Moscow's Ukraine offensive.
"Airborne troops are providing support to advancing assault troops, preventing the transfer of Ukrainian army reserves to the city and the possibility of retreat for enemy units," the Russian defence ministry said in a statement.
"Wagner assault units were continuing high-intensity combat operations to oust the enemy from the central quarters" of the city in eastern Ukraine, according to the statement. The Wagner mercenary group claims to have led the Russian assault on Bakhmut.
Wagner chief Yevgeny Prigozhin said in a statement that it is "too early" to say Russia has Bakhmut surrounded. Recent days appear to have pointed to Moscow's gains in Bakhmut, with several Russian correspondents publishing images from within the city.
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Denis Pushilin, the Russian-installed head of the eastern Ukrainian region of Donetsk, also visited Bakhmut this week. Bakhmut had a population of 70,000 people before Moscow launched its offensive.
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Despite analysts' claims that the city has little strategic value, both Russia and Ukraine are thought to have suffered significant losses in the battle.