The US president said the call was primarily about getting Russia’s co-operation on North Korea but added that Mr Putin made some “very nice” comments about his time in office.
It came as The Washington Post published a 7,000-word expose on the internal battles over Mr Trump’s Russia policy in the last year.
The paper reported that Mr Trump’s refusal to endorse the intelligence agencies' view that Russia hacked the election had undermined attempts to retaliate.
It said that some officials downplay information about Russia in intelligence briefings with the president for fear of triggering his ire.
Some aides have even adopted a “don’t walk that last 5 ½ feet” position, meaning do not enter the Oval Office amid fears Mr Trump could “erupt” or “overrule” decisions, it was reported.
Speaking to reporters on Friday, Mr Trump again dubbed claims he colluded with the Russians a “hoax” and said he wanted to “get back to running the country”.
The president also declined to rule out pardoning Michael Flynn, his former national security adviser charged with lying to the FBI over his conversations with the Russian ambassador.
Mr Trump called Mr Putin, the Russian prime minister, on Thursday to thank him for “acknowledging America’s strong economic performance” at a press conference.
It is the latest in a string of recent chats, including meeting in Asia in early November and discussing Syria in a lengthy call later that month.
Mr Trump’s first year in office has been overshadowed by questions about his campaign’s links to Russia, which are being looked into as part of an investigation into the country’s election meddling.
Since taking office, Mr Trump has made a series of contrasting comments about whether he believes the Russians were involved in disrupting last year’s election – as America's intelligence agencies have concluded.
In a lengthy piece based on interviews with more than 50 current and former US officials, The Washington Post revealed tensions at the very top of the administration over Russia.
There has been no cabinet-level meeting on Russian interference or how to hit back since Mr Trump took office, the paper reported, despite the seriousness of the accusations.
The targeting of the election was estimated to have cost the Russians just $500,000 (£375,000), according to estimates quoted in the report.
One unnamed source told the paper that if you mention Russian interference in Mr Trump’s daily intelligence briefing it goes “off the rails”.
There has also been a battle over whether to return to Russian compounds in America that the US government seized as a punishment under Barack Obama.
Mr Trump’s supporters note that he has signed legislation bringing in new sanctions on Moscow and closed three Russian diplomatic facilities as proof he has not gone easy on the country.
Asked about his call to Mr Putin, Mr Trump said on Friday: “We would love to have his help on North Korea. China is helping. Russia is not helping."
Asked if he would pardon Mr Flynn, Mr Trump said: "I don’t want to talk about pardons for Michael Flynn yet. We'll see what happens.”