The call came Thursday, after Putin used his annual news conference to praise the USA financial markets' rise and other "quite serious achievements" under Trump, whom he said he was on first-name terms with.
Asked whether he was impressed by Trump's performance as U.S. president, Putin said he was not a United States citizen and it is USA citizens who should judge their president's performance.
He said Mr Trump had made "some fairly serious achievements", pointing specifically to the sharp rise in USA stock markets.
On Thursday, Trump called Putin following the Russian President's annual press conference and thanked him for acknowledging the strong economic performance of the United States, according to a readout issued by the White House. "This means they trust what President Trump is doing in this area".
Mr Putin said Moscow understood that Mr Trump's scope to improve ties with Russian Federation was limited by the scandal but he remained keen to try to improve relations. However, he added that the improving state of the American economy under Trump's presidency should be acknowledged, even by his critics.
Trump told reporters Friday that his call with Putin was "great" and that Putin had "said very nice things about what I've done for this country in terms of the economy".
"Look at how the markets have grown".
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The president also endorsed Moore, even after allegations that he sexually abused a 14-year-old girl when he was in his 30s. "He wants to depose Mitch McConnell as Majority Leader even if it costs Republicans Senate control".
Coming amid growing pressure from special counsel Robert Mueller's investigation into possible collusion between the Trump campaign and Russian Federation during the 2016 election, Trump's chummy call with Putin is sure to raise eyebrows.
In a radio interview Mr Macierewicz said the Russian president "should have the courage to take responsibility for what has happened".
"The two presidents also discussed working together to resolve the very risky situation in North Korea", added the White House.
He emphasised that Russian Federation opposes Pyongyang's nuclear bid, but added the USA had "provoked" Pyongyang into developing its nuclear and missile programs by spiking a 2005 deal under which North Korea agreed to halt them.
Mr Trump has repeatedly highlighted surging U.S. stock markets as evidence that his political agenda is succeeding.
A new round of tension around North Korea spiraled on November 29 when Pyongyang carried out a missile launch, the first one since September 15.