The Russian defence ministry said troops had taken control of the neighbouring villages of Progres and Yevgenivka, a few kilometres apart.
Ukrainian President Volodymyr Zelensky acknowledged Kyiv's forces were under pressure in the region during his evening address on Sunday.
"It is extremely challenging in the Donetsk directions, and it is in the Pokrovsk direction that there have been the biggest number of Russian assaults these weeks - the most intense enemy attacks are precisely there," he said.
"Everyone who stops these Russian strikes and destroys this Russian offensive potential is performing one of the most important missions in this war."
On Saturday Russia claimed the nearby village of Lozuvatske, one of nearly a dozen it says it has captured in the Donetsk region this month.
The Kremlin has recently centred its offensive capabilities on the region, which it claimed to have annexed months after launching its invasion of Ukraine in February 2022.
Ukraine's General Staff said on Sunday morning its forces had repelled 29 attacks in the area, where Russia was trying to dislodge its units.
Zelensky on Sunday reiterated calls for allies to provide the country with air defence systems, saying Ukraine has been bombarded by nearly 700 guided bombs and more than 100 Shahed drones this week alone.
"Every concrete decision of our partners to strengthen our force can save lives," he wrote on Telegram.
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