"I don't know who this is and this never happened," he said in a statement released by the White House.
In a declaration, Julie Swetnick, who attended Gaithersburg High School in Maryland, said she observed Kavanaugh drinking excessively at house parties and engaging "in abusive and physically aggressive behavior toward girls."
Swetnick said she witnessed efforts by Kavanaugh and others to get girls inebriated so they could be "gang raped" in side rooms at house parties by a "train" of numerous boys.
"I have a firm recollection of seeing boys lined up outside rooms at many of these parties waiting for their 'turn' with a girl inside the room. These boys included Mark Judge and Brett Kavanaugh."
Judge is a friend of Kavanaugh whom an earlier accuser, Christine Blasey Ford, said was present when she alleges Kavanaugh sexually assaulted her roughly 36 years ago.
In her declaration, Swetnick recounts an alleged incident in approximately 1982 in which she says she was the victim of a "gang rape" at which Kavanaugh was present.
She does not say Kavanaugh participated in the alleged rape or what, if any, role he played, nor does she say where the alleged episode took place.
"During the incident, I was incapacitated without my consent and unable to fight off the boys raping me," Swetnick says. "I believe I was drugged using Quaaludes or something similar placed in what I was drinking."
Avenatti, the lawyer who represents adult film actress Stormy Daniels, is exploring a bid for the Democratic presidential nomination and spoken out against Trump and his policies, making frequent appearances on cable television.
In his tweet, he called Swetnick "courageous, brave and honest" and asked that her privacy be respected.
Ford, a professor from California, has alleged that a drunken Kavanaugh sexually assaulted her when both were teenagers in Montgomery County.
A second accuser, Deborah Ramirez, a classmate of Kavanaugh's at Yale University, told the New Yorker magazine that he exposed himself to her at a party when they were both first-year students.