President Donald Trump has thanked his Russian counterpart Vladimir Putin for remarks he made "acknowledging America's strong economic performance", the White House says.

The two presidents spoke by phone following Mr Putin's annual press conference in Moscow, where Mr Putin was asked to assess Mr Trump's first year in office.

He said Mr Trump had made "some fairly serious achievements", pointing specifically to the sharp rise in US stock markets.

"I'm not the one to evaluate the President's work. That needs to be done by the voters, the American people," Mr Putin said.

"[But] we are objectively seeing that there have been some major accomplishments, even in the short time he has been working.

"Look at how the markets have grown. This speaks to investors' trust in the American economy.

"This indicates the confidence of investors in the American economy. This indicates they have confidence in what President Trump is doing in this sphere.

"With all due respect to those in opposition to President Trump in the United States, these are objective factors."

The White House said Mr Trump spoke with Mr Putin by phone, and thanked him "for acknowledging America's strong economic performance in his annual press conference".

The Kremlin made a point of noting that Mr Trump initiated the call.

Collusion claims, North Korea threat on Putin's agenda

The Russian President delivers the lengthy press conference once a year. ( AP: Pavel Golovkin )

In his press conference Mr Putin accused those investigating potential collusion between Russia and Mr Trump's 2016 presidential campaign of damaging the US political situation, "incapacitating the President and showing a lack of respect to voters who cast their ballots for him".

Mr Putin dismissed those allegations and the idea of a Russia connection as "fabricated".

"What did someone see that was egregious about this? Why does it all have to take on some tint of spymania?" he said.

"All of it was invented by people who oppose President Trump to undermine his legitimacy."

During their call, Mr Trump and Mr Putin also discussed ways to work together to address North Korea's nuclear and ballistic weapons program, the White House said.

Mr Putin had earlier warned the US against using force against North Korea.

He emphasised that Russia opposes Pyongyang's nuclear bid, but added the US 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 said all options remain on the table.

AP