US President Donald Trump has invited his Russian counterpart Vladimir Putin to the US during a phone call and says he'll be glad to see him in the White House, RIA Novosti reports, citing the Russian Foreign Ministry.

The news agency quoted Foreign Minister Sergei Lavrov as saying Trump returned to the subject of an invitation a couple of times during a call last month and that Russia was now expecting Trump to formalise the invitation.

"We proceed from the fact that the US president in a telephone conversation...made such an invitation, said he would be glad to see (Putin) in the White House, would then be glad to meet on a reciprocal visit," said Lavrov, according to a transcript of an interview with RIA on the foreign ministry website.

"He returned to this topic a couple of times, so we let our American colleagues know that we do not want to impose, but we also do not want to be impolite, and that considering that President Trump made this proposal, we proceed from the position that he will make it concrete."

Rolling out a welcome for Putin in the White House could anger Trump's domestic critics, who accuse Russia of hostile acts against Western countries, including the United States.

"I would simply turn your attention to the fact that Donald Trump after this phone conversation has said several times in both Tweets and in words that it is necessary to resolve issues with Russia, we want to have good relations with Russia, this is better than not having good relations, and that only a fool thinks otherwise," Lavrov said. "We also hear this."

Trump and Putin spoke by phone on March 20.