Putin and Trump met in Helsinki earlier this month at a summit, but Trump faced a storm of criticism back home for his handling of the meeting.
Speaking to reporters at a summit of BRICS countries in South Africa, Putin said telephone calls between Moscow and Washington were insufficient and that both sides needed to meet to talk about issues like the Iran nuclear deal, conflicts in the Middle East, and arms control treaties.
"Regarding our meetings, I understand very well what President Trump said. He has a desire to have further meetings, to hold further meetings. I am ready for that. We need for the appropriate conditions to exist, to be created, including in our countries," Putin told a news conference, AFP reported.
"We are ready for such meetings. We are ready to invite President Trump to Moscow. By all means. By the way, he has such an invitation, I told him about that."
"I am ready to go to Washington. I repeat once again, if the right conditions for work are created."
Putin said in the meantime, it was possible that he and Trump would meet on the sidelines of the Group of 20 summit, or another international event.
In a reference to the backlash inside the United States after Trump's performance at the Helsinki summit, Putin said: "Despite the difficulties, in this particular case difficulties linked to the internal political situation in the United States, life goes on and our contacts continue."