The general staff in Kyiv gave the report on Wednesday, saying that the assaults had been repulsed.
Fighting was continuing in many settlements lying on the approach for the Russians to Pokrovsk, some 10 kilometres from the front line.
Russian military bloggers reported that Russian advances in the region.
Pokrovsk, an industrial and mining centre of some 65,000 inhabitants in the Donetsk region before the Russian invasion, is a key Ukrainian supply hub along this section of the front.
Ukrainian Commander-in-Chief Oleksandr Syrskyi has acknowledged that the situation is difficult.
Reports from the Russian side said the defense of Pokrovsk was faltering.
Ukrainian military reports also referred to heavy fighting around Toretsk to the north-east of Pokrovsk.
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