Putin made the comments Friday at a news conference at the summit of leaders of the of BRICs countries in Johannesburg, South Africa.
"(Trump) has a desire to conduct meetings in the future and I am ready", Putin said, extending the invitation and reiterating his desire to go to Washington. It was not immediately clear if Putin was referring to a formal invitation or a verbal one in spirit.
The president has been widely criticized for failing to publicly denounce Russia's interference in the 2016 US election and appearing to accept Putin's denials of such activity.
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Earlier this week, Trump postponed a Washington meeting between the two leaders until next year, citing political fallout over Special Counsel Robert Mueller's ongoing and still fruitless "Russiagate" investigation.
"Russia isn't abandoning the dollar", Putin said in answer to a question about the sharp decline in its holdings of US Treasuries in April and May.
Both Mr Putin and Mr Trump deny the allegations.
Trump has been widely criticized for failing to strongly denounce Russia's election interference and appearing to accept Putin's denials during their joint press conference in Helsinki.
On Friday afternoon, Trump will convene a National Security Council meeting devoted to the issue of election security. No policy changes came out of the summit, Mattis said on Friday, adding he had also not been given new direction on Syria.
By saying that he's willing to go to Washington if conditions are "appropriate", Putin underlines that stance and effectively puts pressure on Trump to try to stamp out opposition.