In an email to Mike Davis, the chief counsel for nominations, Mr Avenatti said he was representing a woman with “credible information” that incriminated Donald Trump’s Supreme Court pick and Mark Judge, Mr Kavanaugh’s former classmate.
He tweeted details of the allegations shortly before it emerged on Sunday night that Senate Democrats were investigating claims Mr Kavanaugh exposed himself to a woman at a party during his first year at Yale University.
Mr Avenatti - lawyer for Stormy Daniels, the adult film star who was paid not to reveal details of an alleged affair with Mr Trump - said the alleged victim, Deborah Ramirez, was not his client.
In an email exchange with Mr Davis, the lawyer said he was ”aware of significant evidence of multiple parties in the Washington DC area during the early 1980s” where Mr Kavanaugh, Mr Judge and others targeted women.
“There are are multiple witnesses that will corroborate these facts and each of them must be called to testify publicly,” he wrote.
He added: “We demand that this process be thorough, open and fair, which is what the American public deserves. It must not be rushed and evidence/witnesses must not be hidden.”
Mr Avenatti posted images on Twitter of his conversation with the chief counsel, who contacted him after he tweeted about having information on Mr Kavanaugh.
He told Politico he represented a group of people who could corroborate claims against the Supreme Court nominee. He said one of the group could be described as a victim and the others were witnesses.
“They went to schools in the same general areas,” he added. ”These house parties were widely attended.”
Mr Kavanaugh and Mr Judge have yet to respond to Mr Avenatti’s claims.
But in a statement issued through the White House on Sunday, Mr Kavanaugh rejected Ms Ramirez’s allegation as “a smear, plain and simple”.
Ms Ramirez attended Yale with Mr Kavanaugh and told The New Yorkerhe thrust his penis in her face, causing it to her touch her, without her consent at a party in the 1983-84 academic year.
“I was embarrassed and ashamed and humiliated,” she added.
Mr Kavanaugh insisted the incident “did not happen”.
He has also denied sexually assaulting a second woman, Christine Blasey Ford, who alleges Mr Kavanaugh tried to force himself on her while they were both teenagers at a party.
According to Ms Ford, Mr Judge was also in the room at the time, but he denies having witnesses any sexual misconduct,
In the wake of the allegations, the top Democrat on the Senate Judiciary Committee has sought the “immediate postponement” of any further action over the judge’s nomination to the Supreme Court.
Mr Trump and the Republican Party had been hoping for Mr Kavanaugh to be confirmed before the court begins its new session on 1 October.
Much is likely depend on the Senate Judiciary Committee’s reaction to the evidence of Ms Ford and Mr Kavanaugh, who will both testify to Congress this week.
Mr Judge has not been called to give evidence, something which Mr Avenatti said was an “absolute” necessity in light of his client’s claims.