Update 5/18/17 1:55 pm: The Associated Press has now reported a correction of an earlier story, after a Senate Committee clarified that they had not received a response from Michael Flynn's legal team.
The Senate subpoenaed the former National Security Adviser last week as part of an investigation of President Donald Trump's ties to Russian Federation.
Burr later walked back his position, saying Flynn still had "a day or two" to comply.
Burr noted later Thursday, though, that it's possible Flynn has not yet definitively decided whether he will comply with the subpoena or not.
Earlier on Thursday, the committee's Republican chairman, Sen. Robert Kelner, Flynn's attorney, stated that the former national security adviser would not "submit to questioning in such a highly politicized, witch-hunt environment without assurances against unfair prosecution".
The House intelligence committee is asking for more government documents - this time about the ouster of FBI Director Jim Comey and conversations he had with President Donald Trump about investigations into Russian meddling in the election. Following the election, Flynn had reportedly discussed with Kislyak the potential of establishing a back channel communication between Trump and Russian President Vladimir Putin that would circumvent the USA national security community, Reuters reports.More news: Watford confirm Walter Mazzarri to leave club at season-end
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The district court route would entail the Senate passing a resolution authorizing civil action that could lead to Flynn being charged with contempt of court.
The committee said it sent a letter requesting material from the FBI and Justice Department related to its ongoing counterintelligence investigation.
Flynn, a retired U.S. Army lieutenant general, was sacked from his position as Trump's national security adviser in February.
Asked about his opinion of the president now, Flynn reiterated his loyalty to Trump.
The Senate committee issued the subpoena for Flynn's records on May 10 after he declined to cooperate with an April 28 request for documents. From there, the contempt charge would be debated in the full Senate and would receive a vote. "No matter what option they take, it's not quick".