Ukrainian officials have said little directly in response to the Russian assertions although a senior security official on Wednesday denied the broad counter-offensive had begun.
Ukrainian troops, she said, had been on the offensive in the area for several days and Russian troops were on a defensive footing, aiming to hold on to their positions.
The Russian defence ministry said on Wednesday Ukraine had mounted attacks near Bakhmut, but that they had been unsuccessful.
Kyiv hopes its counter-offensive will be a turning point in the war but has portrayed assaults under way as localised.
"When we start the counter-offensive, everyone will know about it, they will see it," Danilov, the secretary of Ukraine's National Security and Defence Council, told Reuters.
Persons:
Hanna Maliar, Maliar, Olena Harmash, Pavel Polityuk, Tom Balmforth, Timothy
Organizations:
Kyiv, Wednesday, Press Service, Brigade, Ukrainian Armed Forces, REUTERS, Wednesday Ukraine, Reuters, National Security, Defence Council, Timothy Heritage, Thomson
Locations:
Bakhmut, Russia, Ukraine, Moscow, Donetsk, Donetsk region, REUTERS Russia, Kyiv, Russian