Trump held the call from his Mar-a-Lago estate in Florida on Thursday, just days after his stunning election victory over Democratic rival Kamala Harris, the report said.

Steven Cheung, Trump's communications director, did not confirm the exchange, telling AFP in a written statement that "we do not comment on private calls between President Trump and other world leaders." 

The Post, citing several people familiar with the call who spoke on the basis of anonymity, reported that Trump had reminded Putin of America's sizable military presence in Europe.

They said he also expressed an interest in further conversations to discuss "the resolution of Ukraine's war soon."

Trump also spoke by phone with German Chancellor Olaf Scholz on Sunday and the pair "agreed to work together towards a return to peace in Europe," according to Scholz's spokesman.

Trump's election is set to have a major bearing on the almost three-year Ukraine conflict, as he insists on a quick end to the fighting and casts doubt on Washington's multi-billion dollar support for Kyiv.

Ukrainian President Volodymyr Zelensky spoke with Trump on Wednesday, with the Republican's billionaire backer Elon Musk also notably joining them on the call.

The outgoing Democratic administration of President Joe Biden has confirmed that it will send as much aid as possible to Ukraine before Trump's inauguration on January 20.

On Sunday, Biden's National Security Advisor Jake Sullivan said the White House aims "to put Ukraine in the strongest possible position on the battlefield so that it is ultimately in the strongest possible position at the negotiating table."

This would include using the remaining $6 billion of funding for Ukraine available, Sullivan said.

The Russian government has given a cautious but mostly positive response to Trump's return, with Kremlin spokesman Dmitry Peskov saying Sunday: "The signals are positive... At least he's talking about peace, and not about confrontation."

During his campaign, Trump repeatedly vowed to quickly end the Ukraine war -- even before he is sworn into office -- but without detailing his thinking.

Trump and his allies have railed against US funding for Ukraine, while insinuating that it helps fund a corrupt pro-war nexus of defense companies and foreign policy hawks. 

Trump's eldest son, Donald Trump Jr., shared a clip Saturday on Instagram which showed Zelensky standing next to the president-elect with a caption reading: "POV (point of view): You're 38 days from losing your allowance."

Any quick deal in Ukraine is expected to require Kyiv to cede some of the territory it has lost to Russian invaders in Ukraine's south and east.

A former adviser to Trump, Bryan Lanza, told the BBC on Saturday that Ukraine had to give up any ambition of regaining Crimea, for instance, which was occupied by Russia in 2014.

Kyiv, though facing a manpower shortage and uncertainty over US support, has steadfastly opposed giving up territory and its European allies and weapons suppliers such as Britain and France are known to be nervous about unilateral moves by Trump.

Zelensky has said that giving up land or meeting other demands from the Kremlin would only embolden Putin and provoke more aggression, a view shared by many European allies.

Trump "briefly raised the issue of land" in his call with Putin, the Post reported, without further details.

In recent months, both sides in the war have made moves seen as possible efforts to gain leverage ahead of eventual negotiations, with Ukraine seizing a chunk of Russian territory and Moscow's troops making advances in Ukraine.

This weekend brought the biggest drone attacks yet from both sides. 

Russia launched 145 drones at Ukraine overnight, Zelensky said, while Russia said it had downed 34 Ukrainian drones targeting Moscow on Sunday.