Fighting on the Pokrovsk front was the fiercest anywhere in the war-scarred east, Ukraine's General Staff said in a regular battlefield update, adding that Ukraine had fought off 52 Russian assaults there in the last 24 hours.
Pokrovsk, a transport hub with a pre-war population of 61,000, lies on a main road that serves as an important supply route to other embattled Ukrainian-held outposts.
Some residents have fled during the war, but others have settled there after fleeing elsewhere.
"As of today, the city is 20km from the front line," Serhiy Dobriak, head of the city's military administration, told US broadcaster Radio Free Europe.
To the northeast of the city, Russian troops have advanced even closer to the strategic road.
On Saturday, Moscow claimed control of the village of Lozuvatske, which lies about 6km from it. Ukraine did not comment on the claim.
Dobriak said many of Pokrovsk's residents were reluctantly deciding to evacuate. He put the current population at 60,000, including 4000 children.
"The greatest concentration of enemy attacks was around Zhelanne and Novooleksandrivka," Ukraine's General Staff said, referring to two villages that lie to the east of Pokrovsk.
Russia's defence ministry said its forces had also taken the villages of Prohres, Yevhenivka and Vovche. All three settlements lie east of Pokrovsk. Kyiv did not comment on the claim.
Donetsk's regional governor said at least three people had been killed and three others wounded in Russian shelling of Toretsk, another town reeling from heavy fighting in recent weeks.
Dobriak said civilians from Toretsk were evacuating to Pokrovsk.
Russia launched its full-scale invasion in February 2022 and still occupies nearly a fifth of Ukraine.
Ukrainian forces repelled the Russians from the outskirts of Kyiv early in the war and recaptured territory in the east and south later in 2022.
But since a failed counteroffensive in 2023, Kyiv's troops have mainly been on the defensive in 2024.
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