Coats made those surprise admissions Thursday in his first public comments since rebutting Trump's questioning of the US intelligence assessment that Russian Federation interfered in the 2016 election.
As he spoke, news was breaking out of Washington that Putin had been invited to the White House this fall.
A spokeswoman for House Speaker Paul Ryan says Russian President Vladimir Putin should not expect an invitation to address Congress if he visits Washington in the fall. "Look, the fact is we got along well", he told CNBC in an interview that was recorded on Thursday. What's even more disturbing to me is what might have been said during the men's private meeting- with no one else present. "We discussed lots of great things for both countries, frankly".
It was not clear whether such a meeting would take place before or after the November congressional elections in the U.S.
The remarks came amid the unrelenting domestic criticisms over Trump's performance in Helsinki. He gave no details.
The US intelligence community, which concluded Russian Federation interfered in the 2016 US presidential election under Putin's guidance, has warned the Kremlin is also planning attacks on future US elections - including the midterms.
In a later briefing, White House spokeswoman Sarah Huckabee Sanders insisted that Trump's "no" actually meant he was not taking any more questions from reporters. The U.S. and Russia have been on opposing sides of the conflict in Ukraine, unleashed after a popular uprising against a pro-Russian president and Russia's annexation of Crimea in 2014. She had said on Wednesday the proposal was being considered.
As Americans groped for information about the meeting, Moscow offered snippets of its version on Friday.
Antonov gave details of their discussions on arms control, but said the USA has been reluctant to back Russia's proposals so far.
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A White House meeting would be a dramatic extension of legitimacy to the Russian leader.
"I let him know we can't have this, we're not going to have it, and that's the way it's going to be", Trump said in an interview with the American CBS cable network. He did not spell out what they were.
"Say that again?" Mr Coats asked when told about Trump and Putin's second meeting.
He instead sided with Putin's denial of Russian interference.
The announcement came as the White House sought to clean up days of confounding post-summit Trump statements on Russian interference in the 2016 election.
Huckabee Sanders also announced that the White House would not proceed with a plan to extradite U.S. citizens to Russian Federation for questioning in exchange for Russian Federation allowing its intelligence officials to be questioned as part of the Mueller probe.
Ambassador Anatoly Antonov revealed the discussions amid confusion and concern in the US about what the two presidents agreed behind closed doors.
"Well, you're right, I don't know what happened at that meeting", Dan Coats said at the Aspen Security Forum in Colorado.