"I will not be intimidated into withdrawing from this process", Kavanaugh, a conservative federal appeals court judge nominated by Trump in July for a lifetime job on the top US court, wrote in a letter to the Republican-led Senate Judiciary Committee, which is overseeing the confirmation process.
The woman, 53-year-old Deborah Ramirez, told the New Yorker that she remembers seeing Kavanaugh pulling up his pants after seeing "a penis being in front of my face", during a drinking game at a dormitory party on campus.
Chuck Grassley told reporters Sunday that the committee chairman had no plan to delay a hearing scheduled for Thursday with Christine Blasey Ford, who publicly alleged earlier this month that Kavanaugh sexually assaulted her while they were in high school. The two eyewitnesses who denied the event, he added, were the ones "she alleged were egging Brett Kavanaugh on". The women making the allegations, Trump said, "were coming out of the woodwork and, he said, "in my opinion totally political".
Kavanaugh, now an appeals court judge in Washington, said no witnesses have supported the allegations and called them a "grotesque and obvious character assassination".
Also jumping into the fray was the attorney who represents porn actress Stormy Daniels in her legal fight with Trump.
"It is not accurate to say that those who knew him at the time dispute this", Farrow said on ABC. Ramirez alleges Kavanaugh shoved his penis in her face and exposed himself to her at a party in college.
He said he was not present at a party like the one described by Ford and noted that others Ford said were at the gathering had no recollection of it.
President Trump's Supreme Court nominee Brett Kavanaugh looked to be on a clear path to confirmation.
Kavanaugh could try to indirectly address the Ramirez allegation in the Ford hearing by answering questions about his partying habits and sexual proclivities in a way that gets across he didn't expose himself to Ford.
On Sunday, Senator Dianne Feinstein, the top Democrat on the judiciary committee, urged the panel to halt proceedings in light of the latest allegation. A White House spokesperson also expressed support for Kavanaugh.
Judiciary spokesman Taylor Foy complained that Democrats "actively withheld information" from the Republicans. But some of Ramirez's classmates vouch for her integrity and recall seeing Kavanaugh "frequently and incoherently drunk".
"What we are witnessing is the total collapse of the traditional confirmation process for a Supreme Court nominee", Graham said.
Dr Ford agreed to testify on Thursday after a week-long standoff that saw her forced to leave her California home as she faced death threats and Mr Trump attacked her credibility.
Ford claimed that during her high school years, Kavanaugh, along with another Georgetown Prep student at the time, cornered her in a room at a party. They can all be falsely accused of sexual misconduct - and have their lives destroyed - thanks to feminists and liberal lawmakers who care more about their party's political agenda and ideology than any semblance of due process.