Russian accounts of the fighting said Moscow’s forces have repelled or contained Ukrainian advances in the east and south.
More than 500 days into the invasion, Ukraine’s counter-offensive which began early last month has focused on capturing clusters of villages in the southeast and moving in on Russian forces holding Bakhmut.
Officials on Monday noted advances in both sectors.
“Bakhmut. The enemy is caught in a trap,” General Oleksander Syrskyi, in charge of Ukraine’s ground forces, said bluntly on the Telegram messaging app. “The city is under the fire control of (our) defence forces…the enemy is being pushed out of their positions.”
In the south, General Oleksander Tarnavskyi said on Telegram Ukrainian forces were “on the move” and Russian forces had lost the equivalent of hundreds of men over 24 hours.
President Volodymyr Zelensky has said the counter-offensive, boosted by supplies of sophisticated Western weaponry, is proceeding more slowly than Ukraine had hoped.
Military analysts say Kyiv wanted to point to at least a degree of success to leaders attending the Nato summit in Lithuania starting on Tuesday.
The Russian defence ministry said its forces had repelled Ukrainian attacks in three areas of Donetsk region, including Klishchiivka, the focus of clashes in recent days near Bakhmut.
The ministry also said Russian forces thwarted Ukrainian attacks in the south, including near the village of Rivnopil, which Ukrainian forces said they captured two weeks ago.
Ukraine’s deputy defence minister Hanna Maliar said on Telegram that over the past week Kyiv’s troops had taken back 10.2sq km of territory in the south and 4sq km in the east.
And the Ukrainian military said its troops had now retaken 169sq km on the southern front, and 24sq km around Bakhmut since the counter-offensive began.
Reuters could not verify the situation on the battlefield, and Russia has not acknowledged Ukrainian gains.
Moscow says fighting has been heavy since the counter-offensive began. Its forces still hold swathes of territory in eastern and southern Ukraine following its full-scale invasion on Feb 24, 2022.
Ukraine also reported new Russian attacks on civilian sites.
An attack on a humanitarian aid distribution point in the southeast killed seven people, emergency services said, and two people were killed by Russian shelling in the east.
Russia denies targeting civilian areas.