Ukrainian President Volodymyr Zelensky said that the area around the key city of Pokrovsk remains under severe pressure, with up to 300 Russian servicemen still in the city.
Earlier, Russia said that its troops had advanced in Pokrovsk, a transport and logistics hub that they have been trying to capture for over a year.
The Russian Defence Ministry said its soldiers were destroying what it described as surrounded Ukrainian formations near Pokrovsk's railway station and industrial zone, and had entered the city's Prigorodny area and dug in there.
Reuters could not independently verify the battlefield reports.
The Ukrainian military said Russian troops were not in full control of any district of the city.
"The invaders continue to attack in small groups of up to five soldiers, without using armored vehicles," the operation task force responsible for Ukraine's eastern front line said on Facebook.
Ukraine's 7th Rapid Response Corps said Ukrainian forces had thwarted an attempt to cut off a supply route from Rodynske, to the north.
Pokrovsk had a pre-war population of some 60,000 people, but most civilians fled its ruins long ago.
Capturing it could give Moscow a platform to drive towards Kramatorsk and Sloviansk, the two biggest remaining Ukrainian-controlled cities in the Donetsk region which Russia wants to capture in its entirety.
Mr Zelensky also said that Russia was massing troops near the eastern Ukrainian town of Dobropillia, where Kyiv's forces advanced earlier this year in a successful counter offensive.
Ukraine had recorded recent gains near Dobropillia.
Ukrainian army chief Oleksandr Syrskyi said his forces had stepped up pressure there with the aim of forcing Russia to divert its focus away from Pokrovsk.
He said that his forces captured 188 sq kms held by Russian forces as well as a further 250 sq kms previously controlled by neither side.
If it falls, Pokrovsk will be the most important Russian territorial gain inside Ukraine since Moscow took the ruined city of Avdiivka early last year, after one of the bloodiest battles of the war.
Since then, Russia has made steady but slow gains in intense fighting along the 1,000km front line of a war that has dragged on for more than three years and eight months.
Read more: Ukraine's defence of Pokrovsk reaches crucial phase
No face-to-face peace talks have taken place since July, despite attempts by US President Donald Trump to push for an end to the conflict.
Kyiv says the costly fighting is largely stalemated and its territorial losses marginal; Moscow says it is still making important gains.
Elsewhere, the Russian Defence Ministry said its forces had carried out heavy overnight strikes against a Ukrainian military airfield, a military equipment repair base and military-industrial facilities, as well as gas infrastructure facilities that supported them.
Moscow said its troops had also attacked Ukrainian forces near another city, Kupiansk, and dislodged them from four fortified positions in the industrial zone on the left bank of the Oskol River.
Ukrainian military spokesman Viktor Trehubov said yesterday that Russian attempts to get to the centre of Kupiansk had failed so far, and recent Ukrainian attacks had slowed Russian advances.
