Supreme Court nominee Brett Kavanaugh on Monday lashed out at a report detailing a second allegation of sexual assault against him, calling the accusation "grotesque and obvious character assassination" and vowing not to withdraw his nomination.

In a letter sent to Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, and ranking member Dianne Feinstein, D-Calif., Kavanaugh said he "will not be intimidated into withdrawing from this process."

"The coordinated effort to destroy my good name will not drive me out. The vile threats of violence against my family will not drive me out. The last-minute character assassination will not succeed," he wrote.

Kavanaugh, President Donald Trump's second pick to join the nine-member high court, was first hit with the second allegation in a report from The New Yorker published Sunday night.

The New Yorker and NBC News reported that Kavanaugh is accused of exposing himself to a college classmate, Deborah Ramirez, while they were both at Yale University in the 1980s.

That allegation arrived about a week after reports first surfaced that Christine Blasey Ford, 51, had sent a letter detailing her own accusation of sexual assault against Kavanaugh, 53, that was obtained by Feinstein. The committee's top Democrat said she referred the letter to federal investigators.

Ford alleges that an intoxicated Kavanaugh held her down, covering her mouth and trying to undress her at a gathering when they were both teenagers.

Kavanaugh has categorically denied both the allegations, and said he will testify under oath before the Judiciary Committee in a public hearing on Thursday.

On Sunday, lawyers for Ford appeared to confirm that Ford, too, would testify on Thursday, following days of negotiations with the Judiciary Committee over the date of the hearing, the witnesses present and the cross-examination process.

Read the full text of Kavanaugh's letter: