U.S President Donald Trump said he was willing to work with both Kiev and Moscow to resolve a separatist conflict in eastern Ukraine, following a telephone call with Ukrainian President Petro Poroshenko on Saturday.

The call was the first direct contact between the two leaders since the inauguration of Trump, whose aim to improve relations with the Kremlin has alarmed Kiev while the nearly three-year-old conflict remains unresolved.

It followed fresh artillery attacks in Ukraine's Donbass region, which broke a lull in shelling at a frontline hot-spot that had raised hopes the conflict's worst escalation in months was waning.

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

Trump's open admiration for Russian President Vladimir Putin and campaign pledge to mend ties with Moscow have raised questions over his administration's commitment to maintaining sanctions against Russia for its involvement in the fighting and annexation of Crimea from Ukraine.

Poroshenko's office said the conversation with Trump paid particular attention to "settlement of the situation in the Donbass and achieving peace via political and diplomatic means."

"The two sides discussed strengthening the strategic partnership between Ukraine and the United States," it said in a statement.

Earlier the Ukrainian military and Russia-backed separatists accused each other of launching a new wave of shelling. The past week has seen a flare-up in hostilities in which more than 40 people have been killed in both government- and rebel-held areas.

The escalation near the town of Avdiyivka has left thousands on both sides of the front line with little or no access to power or water amid freezing winter temperatures, prompting aid agencies to warn of a possible humanitarian crisis.

The U.S. and EU sanctions against Russia are linked to accusations from Kiev and NATO that the Kremlin has fuelled the conflict by supporting separatists with troops and weapons - a charge it denies.

Russia says Ukraine instigated the latest surge to firm up Western support, while Kiev accuses the Kremlin of stirring up the violence to test the new U.S. administration's will to involve itself in the crisis.

Trump said his respect for Putin would not affect his foreign policy.

"I respect a lot of people but that doesn't mean I'm going to get along with him. He's a leader of his country. I say it's better to get along with Russia than not," Trump said in an interview with Fox News host Bill O'Reilly on Saturday.