On Thursday, the White House Press Secretary confirmed the leaders were in discussion to meet again in the autumn.
On Twitter Thursday, Trump called the summit "a great success" and cited Ukraine among the areas discussed, without providing details.
What reaction is there to the planned Putin visit?
Among those surprised by the news, Coats, who got the news from MSNBC's Andrea Mitchell as she was interviewing him at the Aspen Security Forum, in Aspen, Colorado. 'That's going to be special, ' he said, to laughs from an audience at a forum. "But I have confidence in both parties", Mr. Trump said as Putin stood at a podium by his side.
Russian President Vladimir Putin on Thursday accused forces in the United States of trying to undermine the success of his first summit with U.S. President Donald Trump, but said the two leaders had begun to improve U.S. -Russia ties anyway.
Media captionTrump says he "misspoke" at Putin summit, but is it too late?
Mr Trump may have been encouraged by recent opinion polling showing that while the public at large is uneasy with Mr Trump's Russian Federation policies, his Republican base - by a sizeable majority - is fine with his performance.
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The president campaigned on closer ties with Russian Federation, a goal that had been thwarted during his first year in office. It took the president several attempts to walk back his comments, amplifying the fallout from his joint appearance with Putin.
Critics complained that Trump was given ample opportunity at a joint news conference on Monday to scold Putin over Russian interference in the USA election but instead accepted Putin's denials over the word of American intelligence agencies.
Confusion over Mr Trump's position took another turn when he appeared to reject suggestions that Russian Federation might try again to influence American elections, prompting a hasty denial by the White House.
The idea of allowing a foreign power to quiz US citizens sparked outrage and the US Senate voted 98-0 against it. Secretary of State Mike Pompeo said it was "not going to happen".
"I bet that soccer ball's been looked at very carefully", Coats said, laughing. In that statement, Coats restated the U.S. intelligence assessment about Russian meddling and Moscow's "ongoing, pervasive efforts to undermine our democracy". That's what would have needed to happen for Putin to cooperate with Mueller's office.
During the panel, Coats said he was still not sure what was discussed at Trump and Putin's one-on-one meeting in Helsinki.
The next day, after a barrage of criticism from Republicans as well as Democrats, Mr. Trump said he misspoke and that he accepts the findings of the USA intelligence community.
Speaking on CNN, Hirono described Trump's assertion that the so-called "Fake News Media" is the "real enemy of the people" - not Russian Federation - as unsettling, and said that the president appeared too willing to embrace Moscow.
Trump appeared to accept the information presented to him that proved Russian Federation meddled in the election, the report states.