A Ukrainian tank rolls on a muddy road near Bakhmut, Donetsk region, on March 29, 2023, amid the Russian invasion of Ukraine. AFP
"Bakhmut is one-third controlled by Ukraine, as international observers have established," Sergiy Leshchenko said in a briefing broadcast by the presidency's Telegram channel.
He denied however that the city was surrounded by Russian forces despite recent claims from a Russian aide in the Donetsk region, where Bakhmut is located, that it was "practically surrounded".
Yevgeny Prigozhin, head of the Wagner paramilitary group spearheading Russia's assault in eastern Ukraine, said last week that his forces were in control of around 70 percent of the city.
Bakhmut -- which once had an estimated population of around 70,000 people -- has been virtually emptied of civilians over months of fierce fighting between Russian and Ukrainian forces.
Kyiv says Bakhmut is key to holding back Russian forces along the entire eastern front.
Both sides have invested heavily in the fight, even though analysts say the city has little strategic value.
The US-based Institute for the Study of War said on Tuesday that Russian forces controlled "roughly 65 percent" of Bakhmut after advancing in recent days.
Ukraine said last week its forces were "managing to stabilize the situation" around Bakhmut and that a counterattack could be launched soon against "exhausted" Russian forces near the city.