The Washington Post first reported Trump warned Putin the US had a "sizeable military presence in Europe" during a phone call between the pair.
The Kremlin has steadfastly denied reports the president-elect Donald Trump and Russian president Vladimir Putin held a call on Thursday, in which Trump urged Putin to not escalate the war in Ukraine.
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"There was no conversation," Putin's Press Secretary Dimitry Peskov told reporters on Monday, adding that the the information was "pure fiction."
"This is the most clear example of the quality of the information that is now published sometimes even in quite respected publications. It completely does not correspond to reality" Peskov said.
The Washington Post reported that the phone call between Trump and Putin took place last Thursday, citing well-placed sources.
The outlet said the president-elect warned Putin of the America's "sizeable military presence in Europe" as he urged restraint in the conflict between Russia and Ukraine. It added Trump expressed interest in a follow up conversation between the pair to resolve Ukraine's war "soon."
The Washington Post has yet to release an official comment on the article.
Trump has previously boasted on the campaign trail that he would end the war in Ukraine in "24 hours" — although has not provided concrete details how he would achieve this.
Putin previously congratulated Trump on his election victory in comments made last Thursday, going so far to praise Trump's courage during an assassination attempt on his life at a rally in Pennsylvania in July.
"He manifested himself in the very correct way, bravely as a man,” Putin said.
The Russian leader added he welcomed Trump's claim he could end the war, but that he was not aware of what Trump's concrete proposals were.
After Trump's election win, Peskov emphasised that Moscow still views the US as an "unfriendly" country and that ties between Russia and the US were at their lowest point in history.
Trump is known to be friendly towards Putin. When he was elected in 2016, Moscow had hopes that Trump would scrap sanctions against the country.
Since then however, Putin has repeatedly noted Trump's first term saw the introduction of the heaviest sanctions against Russia at that time.
Kyiv disputes claim
The Washington Post also claimed that Ukraine's foreign ministry knew about the call and didn't object to the conversation taking place, a claim Kyiv's foreign ministry told Reuters was false.
Ukrainian President Volodymyr Zelenskyy already spoke with Trump during a phone call on Wednesday.
Zelenskyy called Trump to congratulate him on his election victory. Although it isn't known what the pair discussed, SpaceX owner Elon Musk reportedly took part in the call with Zelenskyy thanking him for providing Ukraine with access to the Starlink satellite internet platform.
Trump's election could signal a shift in US foreign policy towards Ukraine. The president-elect is wary of US involvement in foreign conflicts and has previously suggested the money would be better spent domestically.
Current US President Joe Biden is set to meet Trump at the Oval Office on Wednesday to discuss the transition of power, and brief the new president on the wars in Ukraine and the Middle East.
National Security Adviser Jake Sullivan told CBS, "President Biden will have the opportunity over the next 70 days to make the case to the Congress and to the incoming administration that the United States should not walk away from Ukraine, that walking away from Ukraine means more instability in Europe."
This article was updated to include comments from the Dmitry Peskov.