The National Council of Churches said the judge had "disqualified himself" following last week's Senate Judiciary Committee hearing where Kavanaugh denied he had sexually assaulted a woman decades ago.
The group said Kavanaugh, who is Catholic, told "outright falsehoods" to the lawmakers he addressed.
They also criticised his judicial record on a number of issues, including voting rights and health care.
The National Council of Churches does not represent members from the Catholic Church. And US Evangelicals have largely shown support for Brett Kavanaugh.
Meanwhile, a US senate committee has received an FBI report on sexual misconduct allegations against Kavanaugh - Donald Trump's nominee for the Supreme Court.
Senators now have until Friday to review the case involving Kavanaugh and Professor Christian Blasey Ford before an initial vote.
Three women have accused Kavanaugh of sexual misconduct during the 1980s when he was a student. He has denied all claims.
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