The former comedian who crushed incumbent Petro Poroshenko in last month's election met European Commission chief Jean-Claude Juncker before holding talks with the head of NATO Jens Stoltenberg.

Writing on his Facebook page, Zelensky dedicated his trip to the children caught up in the conflict that still rumbles on with Russian-backed separatists in eastern Ukraine which has claimed some 13,000 lives since 2014.

Zelensky renewed his call for Moscow to help end the war, which he said had exposed tens of thousands of children to violence.

"But calls are not enough. This is why my meetings with European leaders will begin with a question: how can we put pressure together on the aggressor? How can we force him to work for peace?" Zelensky wrote.

"I am sure that together we will find a solution. Perhaps not today but we must find one, without fail."

At a press conference with Stoltenberg at the NATO headquarters, Zelenksy vowed to press ahead with his country's pro-Western trajectory.

"The strategic course of Ukraine to achieve full-fledged membership in the EU and NATO... remains unchanged," he said.

"This is the priority of our foreign policy. Ukraine's progress towards high European living and security standards is a demand of Ukrainian society."

Zelensky's election came as a rebuke to the Ukrainian establishment fuelled by popular anger over the war and social injustice.

Both the EU and NATO back the former Soviet state in its tensions with Moscow but also say Kiev has to do more to push through much-needed political and economic reforms.

Ukraine and the West accuse Russia of fuelling the conflict and sending weapons to the insurgents, charges which Moscow denies despite overwhelming evidence to the contrary.

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