The Kremlin on Sunday declined to confirm or deny a US report of a phone call between US President Donald Trump and Russian President Vladimir Putin.

Washington and Moscow have not officially confirmed any communication between the leaders since Trump took office on a pledge to swiftly end the Ukraine fighting.

The New York Post late Saturday reported that Trump told the publication he had spoken on the phone to Putin to discuss bringing an end to the conflict in Ukraine and the Russian told him he "wants to see people stop dying".

The newspaper quoted Trump as saying he had "better not say" how often the leaders have spoken.

Kremlin spokesman Dmitry Peskov in comments to TASS state news agency said he could not confirm or deny a conversation took place, but suggested he was unaware of any such call.

"What can I say about this news item? As the administration in Washington expands its work, many different communications arise. And these communications are held through various channels," the spokesman said.

"And of course, given these multiple communications, I personally can not know something, not be aware of something. Therefore in this case I can't either confirm or deny this."

Peskov previously several times denied reports of conversations between Trump and Putin before the US leader's return to the presidency.

The Kremlin has said it is awaiting "signals" on a possible meeting between Trump and Putin and that no-one in Trump's new administration has been in touch about setting one up.