Since Ford's allegations, two other women have come forward with their own accusations of sexual misconduct against Kavanaugh. Kavanaugh has denied all three allegations. "I ask that she bring those filings forward so that we can learn date, time, and place!"
Republicans are pushing to seat Mr Kavanaugh before the November midterms, when Senate control could fall to the Democrats and a replacement Trump nominee could have even greater difficulty.
"This is ridiculous and from the Twilight Zone", he said in a statement. He and one of the accusers, Christine Blasey Ford, will testify publicly Thursday before the Judiciary Committee. She also said Kavanaugh was present at a 1982 party at which she was raped.
On Wednesday President Trump said he could withdraw Judge Kavanaugh's nomination if he "thought he was guilty of something like this".
Ford, in her testimony, is due to make clear she has no uncertainty about the identity of her alleged attacker, referring to Kavanaugh as "the boy who sexually assaulted me".
Trump had repeatedly called into question the trustworthiness of Ford and the other women accusing Kavanaugh of sexual misconduct but, on Wednesday, appeared to slightly soften his support.
The Republican-controlled committee, led by 11 men, on Tuesday said it had hired Arizona sex crimes prosecutor Rachel Mitchell to question Dr Ford.
"I want to watch, I want to see", he said at a news conference Wednesday in NY.
Ford's statement said she didn't know Kavanaugh well and that she recalls the house party as "almost surely a spur of the moment gathering".
Shortly after, Judge Kavanaugh's Yale university classmate Deborah Ramirez told the New Yorker he had exposed himself at a dormitory party.
During the 2016 presidential campaign, at least 15 women accused Trump of misbehavior ranging from sexual harassment and sexual assault to lewd behavior around women. The committee is set to vote on whether to recommend Kavanaugh's nomination to the full Senate on Friday. Chuck Grassley. "I ask for fair and respectful treatment".