The invite comes two days after the White House said it would postpone Mr Putin's autumn visit until next year.
But Friday, Putin accelerated the timeline, saying that he's ready to come to the White House and revealing for the first time that he's invited Trump to Moscow.
White House spokesperson Sarah Sanders said on Friday morning that "President Trump looks forward to having President Putin to Washington after the first of the year". But National Security Adviser John Bolton said this week that Trump now believes the follow-up sit-down should take place "after the Russian Federation witch hunt is over" and "after the first of the year".
Trump was criticized at home for failing to confront Putin publicly over Moscow's interference in the 2016 US election, and for seeming to contradict his own intelligence agencies on the threat from Russian Federation.
There's also no indication about when Mueller's work might be complete.More news: Some people reckon this "zebra" is actually a donkey
Both leaders have called the Helsinki meeting successful, and Mr Putin rounded on US summit critics earlier this month for wanting to sacrifice the US-Russia relationship over "narrow party interests".
Her statement was in response to Mr Putin, who earlier had said at a news conference in South Africa that he was "ready" for a follow-up meeting with President Trump.
But speaking to reporters in South Africa, where he was attending a summit of BRICS nations, Putin said another meeting with Trump was still on the agenda. "Be my guest. He has such an invitation, I told him that".
"I am ready to go to Washington".
There, Trump was widely criticized for appearing to back Putin's denial that Russian Federation interfered in the 2016 USA election - statements Trump subsequently walked back.
Putin said that, in the meantime, it was possible that he and Trump would meet on the sidelines of the Group of 20 summit in Argentina in November, or at another worldwide event. However, efforts to achieve a detente have been fiercely resisted by the US lawmakers, including some in Trump's own Republican Party, who accuse him of being too friendly towards Putin. Among the issues Putin said he's eager to talk about are nuclear arms control, conflicts in the Middle East, and the Iran nuclear deal.