The crisis in the town of Avdiyivka appeared to have eased on Monday as a power line was restored and shelling was less on the weekend.
Ukraine on Sunday said that separatist artillery attacks had significantly lessened, although pro-Russia rebels said the military had kept up its barrage.
The streets of Avdiyivka were relatively quiet on Sunday, with no shelling reported, according to AFP.
The Kiev government on Monday said it had restored power to Avdiyivka after shelling damaged the line into the town close to separatist-held Donetsk.
At least 33 people including civilians were killed in fighting in the past week in the worst violence the region has seen in two years.
With an estimated 18,000 people running short on supplies, authorities say they may evacuate Avdiyivka if the situation worsens.
According to the UN, the death toll in the fighting across the separatist region has reached nearly 10,000 since it started in April 2014.
The most recent clashes threaten to derail a 2015 ceasefire.
TRT World 's Christine Pirovolakis has more.
EU foreign ministers to discuss Ukraine crisis
The European Union's foreign policy chief Federica Mogherini will host EU foreign ministers on Monday to assess progress in the implementation of reforms in Ukraine.
As part of ongoing efforts to restore peace in the country, the Ukrainian government has agreed to devolve powers to local authorities. But the decentralisation process has angered many Ukrainian nationalists, who oppose giving concessions to the the rebels.
Ukrainian President Petro Poroshenko on Friday blamed Russia, which backs the separatists, for the latest flare-up in hostilities.