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A top rebel commander in Ukraine has reportedly been killed in a car explosion. (AFP file image)

A top rebel commander in eastern Ukraine was killed along with another person when their car exploded, rebels have reported.

The rebels' Lugansk Information Center reported today that Lugansk People's Militia commander Oleg Anashchenko died in the explosion along with an unnamed person.

Ukraine's military, meanwhile, said three soldiers were killed in shelling over the past day.

Fighting between government forces and Russia-backed separatist rebels has escalated over the past week in eastern Ukraine, killing at least 33 people, including civilians, and wounding several dozen.

More than 9,800 people have died since the war began in April 2014.

Ukrainian President Petro Poroshenko spoke late Saturday with US President Donald Trump, who he said expressed "deep concern" over the escalation.

During the call, a statement issued by Mr Poroshenko's office said the two leaders "noted the urgent necessity of establishing a complete cease-fire."

The Ukrainian president thanked Mr Trump for his "strong support for the sovereignty and territorial integrity of Ukraine."

Mr Poroshenko has cast the outburst of fighting as an argument for continuing Western sanctions imposed on Moscow for its actions in Ukraine.

The White House said Mr Trump had a "very good call" with Mr Poroshenko.

"We will work with Ukraine, Russia, and all other parties involved to help them restore peace along the border," Mr Trump said in a statement.

The government-held town of Avdiivka, just north of the main rebel-controlled city of Donetsk, has been the focus of the fighting.

A temporary cease-fire had been called to allow workers on both sides to restore electricity to freezing residents as shelling eased for much of the day. But the Ukrainian military said rebel forces began a mortar barrage of Avdiivka in the evening.

The daily shelling has left locals in the industrial town of about 35,000 traumatized.

Mr Trump's repeated promises to improve relations with Russia have fueled concern in Ukraine that Washington would back off some of the sanctions.

However, the US ambassador to the United Nations, Nikki Haley, has said sanctions imposed for Russia's 2014 annexation of Crimea will remain.

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Ukraine rebels claim top commander dies in car bombing - 9news.com.au