"In the sworn affidavit posted by Avenatti, Swetnick says she was a victim of a "'gang" or "train'" rape and Kavanaugh was present.
Christine Blasey Ford is scheduled to testify to the Judiciary Committee on Thursday about her allegations that Kavanaugh assaulted her at a 1982 party.
"There has been a frenzy to come up with something - anything, no matter how far-fetched or odious - that will block a vote on my nomination", Kavanaugh says, in the testimony released by the Senate Judiciary Committee.
In an email to Mike Davis, the Chief Counsel for Nominations, Avenatti says he has "significant evidence" of house parties in Washington D.C. during the early 1980s "during which Kavanaugh, Mark Judge and others would participate in the targeting of women".
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"It will relate to how they behaved at countless house parties, " Avenatti said. "I never did anything remotely resembling what Dr. Ford describes". She alleged Kavanaugh and his friends "spiked" the drinks of girls at house parties.
"This morning Michael Avenatti provided a declaration to the Judiciary Committee".
Avenatti didn't disclose how his client met Kavanaugh and Judge or reveal details on the timing of the alleged misconduct.
Swetnick did not identify who allegedly raped her nor did she accuse Kavanaugh or Judge of raping her or physically assaulting her in any way.
FOX 5 has not been able to corroborate Swetnick's allegations and is investigating the claims. Kavanaugh has categorically denied the allegations against him.
"We demand an immediate FBI investigation into the allegations", he tweeted.
A spokesperson for the Time's Up movement later issued a statement calling for Kavanaugh to withdraw: "His confirmation would compromise the integrity of the court for generations to come", he said.