Mr. Putin and Mr. Trump met in Helsinki earlier this month at a summit, but Mr. Trump faced a storm of criticism back home for his handling of the meeting.
The president, his son, his lawyers and other administration officials have repeatedly said Trump did not know about the meeting until news of it broke in July 2017.
The White House statement came after National Security Adviser John Bolton said earlier this week that a meeting with Putin in the USA would be pushed off until next year - after the conclusion of the Federal Bureau of Investigation probe into Russian interference in the 2016 election.
"I am ready for that. We need for the appropriate conditions to exist, to be created, including in our countries", Putin said at a news conference.
But amid all of the questions about who knows what, here's what we know about the Trump Tower meeting?
But the possibility of a Trump trip to Moscow emerged Friday after Putin said he was ready to invite Trump _ or to visit Washington if conditions are right. "He has this invitation already and I told him about it", according to CNN.
The Secret Service said the ball underwent a routine security screening.
"They want President Trump to deliver on his election promises, to make the relationship better with Russian Federation, but they also see that he's not going to be able to do that if he continues to perform like he performed in Helsinki when standing next to President Putin".
Last week, Mr Trump had suggested that Mr Putin should visit Washington this autumn.
Trump denies there was any collusion.
Kaitlan Collins: "Why has Vladimir Putin not accepted your invitation, Mr. President?"
Efforts by both Trump and Putin to achieve detente have been fiercely resisted by USA lawmakers, including some in Trump's own Republican Party, accusing him of being too friendly toward Putin, whom they consider an adversary of the United States. "In 2021, the New START treaty expires", he said, referring to a nuclear arms control treaty. "We are not going to comment further on security procedures". "We need to minimise risks, we see what's happening with sanctions. I don't think so - it's not a secondary issue".
President Trump received an update from his National Security Council Friday afternoon on the government-wide effort to prevent foreign interference in the USA election system.