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.
Ukrainian President Volodymyr Zelenskiy told reporters Russia was massing troops by the nearby town of Dobropillia, where Ukrainian forces advanced earlier this year in a successful counteroffensive.
Zelenskiy described the situation in Dobropillia as complicated.
Russian forces, he said, had lost the initiative in the area but were bringing in more troops.
He said Pokrovsk remained under severe pressure although Russian troops had made no gains in the past day.
He said up to 300 Russian servicemen were still in the embattled city.
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 armoured vehicles," the operation task force responsible for Ukraine's eastern front line said on Facebook.
Reuters could not independently verify the battlefield reports from either side.
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 about 60,000 people but most civilians fled its ruins long ago.
Capturing it could give Russian forces 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.
If it falls, Pokrovsk will be the most important Russian territorial gain inside Ukraine since the Kremlin's forces took the ruined city of Avdiivka in early 2024 after one of the bloodiest battles of the war.
Since then, Russia has made steady but slow gains in intense fighting along the 1000km front line of a war that has dragged on for more than three years and eight months.
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.
Ukraine says the costly fighting is largely stalemated and its territorial losses marginal; Russia 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.
Russia 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.
Zelenskiy said that up to 60 Russian soldiers remained in Kupiansk and Ukrainian forces were trying to clear them.
Ukrainian military spokesman Viktor Trehubov said on Sunday that Russian attempts to get to the centre of Kupiansk had failed so far and recent Ukrainian attacks had slowed Russian advances.
