Donald Trump has said he could meet with Vladimir Putin "very soon," following what the US president described as highly productive talks in Moscow between his special envoy and the Russian leader.

The potential summit was discussed in a call between Trump and Ukrainian leader Volodymyr Zelensky that, according to a senior source in Kyiv, included Nato Secretary General Mark Rutte and the leaders of Britain, Germany and Finland.

"There's a good chance that there will be a meeting very soon," Trump told reporters at the White House, when asked when he would meet the Ukrainian and Russian leaders.

He gave no indication where the meeting with Putin might take place.

The New York Times and CNN, citing people familiar with the plan, said Trump plans to sit down with Putin as early as next week, and then wants a three-way meeting with the Russian leader and Zelensky.

Trump's phone call with Zelensky came after US envoy Steve Witkoff met Russian leadership in Moscow earlier in the day for talks described by the Kremlin as "productive" – with Trump's deadline looming to impose fresh sanctions over Russia's war in Ukraine.

"Great progress was made!" Trump wrote on his Truth Social platform, adding that afterward he had briefed some European allies.

"Everyone agrees this War must come to a close, and we will work towards that in the days and weeks to come," he said.

Minutes later, however, a senior US official said that "secondary sanctions" were still expected to be implemented on Friday.

Trump, who had boasted he could end the conflict within 24 hours of taking office, has given Russia until Friday to make progress towards peace or face new penalties.

Three rounds of Russia-Ukraine talks in Istanbul have failed to make headway on a ceasefire, with the two sides far apart in their demands.

Russia has escalated drone and missile attacks against its neighbor, a US and European Union ally, to a record high and accelerated its advance on the ground.

"A quite useful and constructive conversation took place," Putin's aide Yuri Ushakov told journalists after the three-hour meeting with Witkoff.

The two men exchanged "signals" on their positions, Ushakov said, without elaborating.

Zelensky confirmed his call with Trump and confirmed European leaders had taken part, although he did not name them.

Trump has voiced increasing frustration with Putin in recent weeks over Russia's unrelenting offensive.

The White House has not officially outlined what action it would take against Russia, but Trump told reporters it plans to impose "a lot more secondary sanctions" targeting Russia's key trade partners, possibly targeting China.

Earlier in the day he had ordered steeper tariffs on Indian goods over New Delhi's continued purchase of Russian oil. (AFP)