"I'll be his worst nightmare, but I don't think it'll be that way," Trump said about Putin. "I actually think we'll have a good relationship."
In the same interview, Trump blasted his predecessor, President Barack Obama, for having been a "total patsy" for Russia — while claiming he has been "far tougher on Russia than any president in many, many years."
"Maybe ever," Trump added.
But Trump also said he valued the opportunity to improve the United States' relationship to Russia, even after American intelligence agencies have said that Russia repeatedly tried to interfere in the 2016 U.S. presidential election.
""Getting along with President Putin, getting along with Russia, is positive, not a negative," Trump said.
Later Thursday, White House press secretary Sarah Huckabee Sanders tweeted that Trump asked National Security Advisor John Bolton to invite Putin to Washington in the fall.
The president's comments came three days after he met with Putin in Helsinki, where his comments at a joint press conference with the Russian strongman drew widespread criticism both from Democrats and from his fellow Republicans.
Under questioning from reporters, Trump refused to criticize Putin for the election meddling, and suggested that it was an open question as to whether the former KGB spy Putin's denials of such hostile action were as credible as the findings by American intelligence services.
The president's interview with CNBC also came on the heels of a New York Times report that said Trump, two weeks before his inauguration in January 2017, had been shown extensive evidence that Putin personally ordered interference in the 2016 U.S. elections.