By Susan Cornwell and Jonathan Allen

WASHINGTON/NEW YORK (Reuters) - The Democratic minority on a U.S. congressional committee investigating the attack in Benghazi, Libya, intend to defy the committee's Republican leaders by releasing the transcript of a closed-door interview with a former senior aide to Hillary Clinton, they said on Monday.

The announcement comes six days after Kevin McCarthy, the leader of U.S. House Republicans, went on television to boast that the federally funded investigation had successfully dented Clinton's poll numbers as she runs for the Democratic presidential nomination.

He later clarified that he had not meant to suggest that harming the Democratic front-runner's chances at winning the November 2016 election was the committee's purpose.

This has not stopped Democrats, including Clinton herself, from seizing on his comments as confirmation of what they have believed all along.

"Despite claims that the Committee would be run with integrity, Republicans have engaged in a series of selective leaks of inaccurate and incomplete information in an effort to attack Secretary Clinton," the committee's Democrats wrote in their letter on Monday to Trey Gowdy, the committee's Republican chairman.

To combat this, the Democrats said they would start releasing transcripts from the committee's closed-door interviews with witnesses "to correct the record," beginning with that of Cheryl Mills.

Mills was Clinton's chief of staff at the State Department at the time of the Sept. 11, 2012 attack by militants on the U.S. diplomatic compound in Benghazi. J. Christopher Stevens, then the U.S. ambassador to Libya, was among four Americans killed.

Gowdy, who has said the committee is not politically motivated, did not immediately respond to requests for comment. Nor did spokesmen for Clinton, although Clinton has been adamant that her testimony, due to be given to the committee on Oct. 22, be in a public hearing. Mills also sought to have the transcript of the day-long interview she gave the committee in August be released.

Democrats on the committee said they would give Gowdy and his Republican colleagues five days to notify them whether any portion of Mills' transcript "be withheld from the American people," after which they would release it.

(Reporting by Jonathan Allen; Editing by Jonathan Oatis)