He invoked his legal right against self-incrimination, his lawyers told the committee.
The Senate Intelligence Committee is investigating possible links between the Trump campaign and Russia.
Michael Flynn stood down in February after it emerged he lied about his contacts with the Russian ambassador.
The Senate committee issued a subpoena – a legal summons – two weeks ago to obtain documents about his contacts with Russians dating back to June 2015.
Two other former top Trump aides – Paul Manafort and Roger Stone – have complied with the committee’s request for information, it was reported on May 22.
The panel, another congressional committee and the FBI are investigating claims that Russian hackers tried to help Donald Trump win last November’s presidential election, and whether members of his campaign colluded with the alleged Russian conspiracy.
Michael Flynn’s name has cropped up repeatedly in the matter, but his letter to the Senate panel emphasizes his refusal to comply is not an admission of wrongdoing.
The former Army lieutenant general is invoking the 5th amendment to the US constitution, which protects Americans from being legally compelled to testify against themselves in a criminal case.
The letter said Michael Flynn’s decision was a response to the current political climate and an “escalating public frenzy against him”.
His attorneys argued that “any testimony he provides could be used against him”.
Republican Senator James Lankford, who serves on the Senate Intelligence Committee, tweeted: “It is Mike Flynn’s right to plead the 5th.
“We will get to the truth one way or another.”
If Michael Flynn continues to refuse to comply, it is thought Senate investigators could vote to hold him in contempt of Congress, or even refer his case for possible criminal charges.
Michael Flynn’s legal representative has previously demanded immunity from “unfair prosecution” before his client testifies.
Last week the committee’s chairman, Senator Richard Burr, told reporters that Mike Flynn was “not co-operating” with the investigation.
Shortly after Michael Flynn left the White House, the Department of Defense also launched an inquiry into payments he received for a speech in Russia and for lobbying on Turkey’s behalf.
Former acting Attorney General Sally Yates testified to senators earlier this month that she had warned the White House 18 days before Michael Flynn was fired that he was vulnerable to Russian blackmail.
Michael Flynn misled the White House about discussing US sanctions against Russia with Moscow’s envoy, Sergei Kislyak, before DonaldTrump took office.
President Trump injected a fresh impetus into the Senate investigation after he himself met the Russian ambassador and foreign minister in the White House earlier this month.
Donald Trump said in that encounter that he had just fired the FBI director because he was a “real nut job” and his dismissal eased “a great pressure because of Russia”, the New York Times reported.
During the Oval Office chat, which media were not invited to cover, Donald Trump also reportedly divulged secret information on the military campaign against ISIS.
Israel was reportedly the source of that sensitive intelligence.
However, while in Jerusalem on May 22, President Trump told reporters repeatedly that he “never mentioned the word Israel” in his meeting with Russian officials.
Former FBI director Robert Mueller was appointed last week as special counsel to lead the FBI investigation following President Trump’s firing of the law enforcement agency’s director, James Comey.
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