AFP was unable to verify the status on the ground in the eastern town, which has turned into the longest and bloodiest fight since Russia invaded Ukraine last year.
Russian troops have been battling since last summer to capture the town, which had a pre-war population of 70,000, and whose fall would now mostly present a symbolic victory for Russia.
The Russian army said its airborne troops were "blocking the transfer of Ukrainian army reserves to the city and the possibility of retreat for enemy units."
It also said that Wagner mercenary units were advancing in Bakhmut.
But the Ukrainian army told AFP it had communication with its troops inside Bakhmut and was able to send them munitions.
"This does not correspond to reality," Sergiy Cherevaty, spokesman for Ukraine's eastern forces said, referring to Russia's claims.
"We are able to... deliver food products, ammunition, medicines, all that is necessary, and also to recover our wounded."
The Ukrainian general staff nevertheless acknowledged a "difficult" situation in Bakhmut.