Ukrainian officials say two civilians were killed when the separatists fired on the government-held frontline town of Avdiivka.
The separatists say two civilians died as the government shelled the rebel stronghold of Donetsk.
At least 15 people have been confirmed killed in the worst fighting for weeks.
A number of people have been injured since the clashes intensified over the weekend.
There are fears that the actual death toll could be much higher.
Ukraine accuses Russia of launching an offensive, while Moscow says Kiev is seeking to push back the separatists from their positions in the Donetsk and Luhansk regions.
The two countries again traded accusations during an urgent UN Security Council session to discuss the conflict which has claimed the lives of more than 9,700 people since 2014.
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On Thursday evening, Pavlo Zhebrivsky, the head of the Ukraine-controlled Donetsk regional administration, said a man was killed when a humanitarian aid point in Avdiivka was hit.
He later said a woman had died of her wounds after the rebels shelled an area near a school in the town.
Avdiivka, whose population is estimated to be about 22,000 people, has been left without water and electricity in freezing conditions because of the shelling.
Ukrainian officials and aid agencies have warned of a possible major humanitarian crisis, declaring a state of emergency in the town.
Meanwhile, rebel officials said Donetsk was under heavy shelling late on Thursday, and two civilians had been killed.
There are also reports that a powerful blast in the city destroyed a building.
A number of Donetsk residents have also been left without water.
The conflict in eastern Ukraine erupted after Russia annexed Ukraine's southern Crimea peninsula in March 2014.
A ceasefire was eventually agreed in February 2015 but there have been frequent violations. The latest truce began on 23 December.
The US and EU imposed sanctions on Russia in response to its actions in eastern Ukraine and Crimea.
Russia has repeatedly denied sending troops and weapons into eastern Ukraine, but admits that Russian "volunteers" fight alongside the rebels.
Shelling has raged on after nightfall in eastern Ukraine, with both government troops and pro-Russian rebels reporting new casualties.