Mr Putin and Mr Trump sat down for their first summit in Helsinki on Monday, an event that sparked a storm of criticism in the United States after Mr Trump refused to blame the Russian leader for meddling in the 2016 USA election, something Mr Putin denies.
Mr. Trump, asked by "CBS Evening News" anchor Jeff Glor on Saturday whether he agrees with Coats' assessment of the risks of a cyber attack, said he didn't know if he did and would have to review that assessment.
"Say that again?" Mr. Coats asked in surprise, as the audience laughed.
Trump and Putin praised US-Russia military ties at the joint press conference following their summit, and mentioned the possibility of greater cooperation in the seven-year war in Syria that has killed about half-a-million people.
Controversy has raged over the Helsinki summit, with Mr Trump having to correct his own words from the press conference which followed it. Trump has gone back and forth on what was said during the meeting and whether he believes Russian Federation meddled in the election on his behalf.
"I don't see any reason why it would be", Trump said in Helsinki.
Donald Trump reiterated the statement that Democrats and the press are the enemy just before his summit with Putin kicked off earlier this week, launching into them in a tweet while he was en route to Helsinki.
Trump's remarks on Wednesday are not the first time he's brushed against U.S. intelligence assessments of the 2016 election meddling.
US intelligence officials have said Russian election interference efforts are continuing and now target the upcoming congressional elections in November.
An investigation into possible interference by American special counsel Robert Mueller, part of which is focused on whether there was any collusion between Trump's campaign team and Russian officials, is ongoing.
Facing a backlash of bipartisan criticism, the White House on Thursday said Trump "disagrees" with Putin's offer.
Russian Federation was also seeking to interview Michael McFaul, another Putin critic who was USA ambassador to Moscow under President Obama. She said the U.S. hopes Putin will have the Russians indicted on charges brought by the U.S. Department of Justice "come to the United States to prove their innocence or guilt".
The Americans in question include former U.S. ambassador to Russia Michael McFaul and alleged crimes include fraud and corruption. She said the USA hopes Putin will have the indicted Russians "come to the United States to prove their innocence or guilt".
McFaul, who served as ambassador to Russian Federation under former President Barack Obama from 2012 to 2014, expressed his gratitude after the vote.
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