Kavanaugh and Christine Blasey Ford, the woman accusing him of a past sexual assault, are expected to testify Thursday before the Senate Judiciary Committee amid a media frenzy that could surpass the Clarence Thomas-Anita Hill hearings in 1991.
Lawyer Michael Avenatti provided a statement from his client to the committee.
All 10 Democrats on the Judiciary Committee also urged Kavanaugh to withdraw if the Federal Bureau of Investigation does not investigate the allegations. In a sworn statement prepared by Avenatti and submitted to committee, Swetnick said that Kavanaugh and his friend Mark Judge were present at a party where she was drugged and "gang raped". "I'm confident we are going to win", McConnell said, adding the vote would come "in the very near future".
The statements, first reported by USA Today, will likely be used by Ford's lawyers during a Thursday confirmation hearing that could help determine the fate of Kavanaugh's nomination.
Avenatti is best known as the lawyer for Stephanie Clifford, the adult film star known as Stormy Daniels who says she had an affair with Trump before he was elected president.
Kavanaugh and his chief accuser Christine Blasey Ford, who says Kavanaugh assaulted her in high school, are set to testify Thursday before the Senate Judiciary Committee. So far the White House and Republicans on the Senate Judiciary Committee have declined to ask for the FBI to investigate the decades-old allegations against Kavanaugh.
In the written testimony released on Wednesday by the committee, Mr Kavanaugh says he has "never sexually assaulted anyone - not in high school, not in college, not ever".
Ford accused Kavanaugh of trying to force himself on her during a party while she was 15 and he was 17. "It's possible they will be convincing".
Support for Supreme Court nominee Brett Kavanaugh has fallen to its lowest levels since President Donald Trump announced his selection in July, according to new polling. He said he doesn't know a lot about these accusations yet, but he did at one point also say he thought they were false.
Two affidavits, from Ford's husband Russell Ford and from the coach of their son's baseball team, say Ford named Kavanaugh as the alleged assailant.
"Laughing, how they fooled you all", Trump said to reporters.
FILE - A sign requesting privacy and stating she has no comment is posted outside the home of Deborah Ramirez in Boulder, Colo., Sept. 24, 2018.
Believing this is a lie requires you to believe that Ford would choose to sacrifice the placid and by all accounts rewarding life she's been leading as a university professor, wife and mother in order to cast false aspersions on someone with whom she's had no contact for well over 30 years. A Grassley spokesman later reiterated the hearing will go on as scheduled.
"Brett's assault on me drastically altered my life". He accused Republicans of continually changing conditions of how Ramirez could tell her story.
As a result, the president claimed he may have trouble attracting people to be Supreme Court justices.
Republicans have rejected any further delays in the confirmation process, scheduling a judiciary committee vote for Friday, which will be followed by consideration by the full Senate.
Trump on Wednesday faulted Republicans for not pushing the nomination through the Senate, which must confirmation Supreme Court appointments, more quickly.