The death toll from the latest escalation in fighting in Ukraine rose to 19 on Wednesday as international alarm rang out over the spike in bloodshed in the European Union's back yard.

Government forces and Russian-backed separatists exchanged mortar and rocket fire for a fourth day around the flashpoint eastern town of Avdiivka just north of the rebels' de facto capital Donetsk.

The Ukrainian military said three of its soldiers had died overnight while the rebels said four civilians had been killed.

Hundreds of mourners laid flowers on Kiev's Independence (Maidan) Square as Ukrainian servicemen carried the coffins of comrades killed in the latest surge of fighting.

The clashes in Avdiivka have left more than 20,000 people without heat or water in freezing winter weather with no signs of relief in sight.

The fighting comes at a potential watershed moment for Ukraine as fears mount in Kiev that staunch US support could be set to wane with President Donald Trump looking to mend ties with Russian counterpart Vladimir Putin.

An emergency UN Security Council meeting on Tuesday called for an immediate end to fighting in a near three-year conflict that has plunged Moscow's relations with the West to a post-Cold War low.

The council expressed "grave concern" about the resumption of serious battles in one of Europe's bloodiest conflicts since the 1990s Balkans wars.

"The intense fighting around Avdiivka in the last few days... is a blatant violation of the ceasefire, as stipulated by the Minsk agreements," the EU said on Tuesday.

The deal signed in the Belarusian capital Minsk in February 2015 has been repeatedly broken but is still seen as the best hope of bringing peace to a country that was once a bridge between Russia and the West.

The war began shortly after pro-Western protesters on Maidan Square ousted Ukraine's Russian-backed president in February 2014 and Moscow responded by seizing Crimea.

- 'Kids woken by shelling' -

The industrial hub of Avdiivka came under its first assault on Sunday by rebels seeking to recapture territory along the frontline dividing the rival sides.

Residents such as 62-year-old Larysa were packing up to find shelter from the cold and violence.

"We slept very badly last night, the kids were awoken by shelling," she told AFP as she left town with her two granddaughters.

"A shell landed under our window but thank God it did not explode."

Pro-Kiev Donetsk region administrator Pavlo Zhebrivskiy said Ukraine had received a Russian assurance that a truce would go into immediate effect but there was no confirmation from Moscow or Kiev.

He said on Facebook that said nearly 80 people had either left or been evacuated from Avdiivka so far.

The fighting has severely damaged a coke plant that provides heating for the blue-collar town of some 25,000 people.

The Organization for Security and Cooperation and Europe (OSCE) is responsible for monitoring ceasefire violations and organising peace talks between envoys from Russia and Ukraine.

Its Ukraine mission said 22,000 people had been left without heating or water and electricity as temperatures dropped to minus 20 degrees Celsius (minus four degrees Fahrenheit).

Zhebrivskiy said the level of heating in the town remained low. He added that the town had access to water but that pressure systems were too weak to make it accessible in the higher floors of tall buildings.

The conflict has killed nearly 10,000 people -- more than half of them civilians -- since it erupted in April 2014.

Russia gives political backing to the rebels but has denied accusations from the West and Kiev that it is directing the insurgency or has sent troops into the war zone.

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