In addition to this story, there's new information in the article from the allegations of Christine Blasey Ford. She attended Yale with Justice Kavanaugh, where she studied sociology and psychology, the magazine said.
As for Kavanaugh, he tells the New Yorker.
That response seemed a setback to Ford supporters' efforts to corroborate her claim.
"Despite actual threats to her safety and her life, Dr. Ford believes it is important for senators to hear directly from her about the sexual assault committed against her", Ford's attorneys Debra Katz, Lisa Banks and Michael Bromwich said in a statement.
The third, Patrick J Smyth, issued a statement on Wednesday denying any knowledge of the party, and going on to praise Kavanaugh as a "person of great integrity".
Terms of their appearances are still being negotiated, but several details have been resolved. "I remember a penis being in front of my face", she said, describing the alleged event. "Judge Kavanaugh has unequivocally denied Dr. Ford's allegations".
Kavanaugh denies the allegations and has said he would testify to clear his name.
The president's comments infuriated Democrats, dismayed many Republicans and risked further alienating women voters ahead of the November 6 mid-term elections, in which Democrats have a chance to win control of the House and perhaps the Senate.
Mr Grassley's staff also agreed to let Ms Ford testify without Mr Kavanaugh in the room, for there to be only one camera in the room, "adequate" breaks and a high security presence.
Lawyers for Blasey are also pressing Republicans to subpoena outside witnesses, notably Mark Judge, a friend of Kavanaugh's who Blasey says was in the room when the assault occurred.
In a preparation session on Tuesday, Kavanaugh faced more than a dozen White House aides in the Eisenhower building, during which aides played different senators for more than two hours.
The official claimed it was a "clever way" to continue negotiations "without committing to anything".
Supreme Court nominee Brett Kavanaugh faces a second allegation of sexual misconduct after another woman came forward accusing him of inappropriate sexual behaviour during his college years at Yale University.
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Democratic Senator Dick Durbin of IL, also a Judiciary Committee member, questioned why Ford would have come forward if the allegation wasn't true.
Ms Ford's lawyers said it was still unclear who will ask questions, as Republicans were trying to hire an outside female counsel who could take over the questioning.
Supreme Court nominee Judge Brett Kavanaugh seen Tue., Sept. 4, 2018, in Washington, D.C.
Pence tells a gathering of evangelical activists in Washington that the appeals court judge's record and career deserve "the respect of every member of the United States Senate".
Kavanaugh's confirmation appears to turn mostly on the support or opposition of three Republican senators: Jeff Flake of Arizona, who is on the Judiciary panel that Republicans control 11-10; Susan Collins of ME and Lisa Murkowski of Alaska.
Pence made no reference to Christine Blasey Ford, whose accusations about Kavanaugh's behavior 35 years ago have roiled the confirmation.
The new deadline is 2:30pm Saturday. "Enough is enough. Brett Kavanaugh needs to withdraw immediately".
The committee chairman, GOP Sen.
The denial from the fourth witness became public shortly after staffers for Judiciary Chairman Chuck Grassley (R-Iowa) reached a tentative agreement with Ford's lawyers on a date, time, and a set of conditions for Ford's testimony.
Here's what Grassley says in a tweet: "I feel like I'm playing 2nd trombone in the judiciary orchestra and Schumer is the conductor".
Supreme Court nominee Brett Kavanaugh is accused of sexual assault. The two attorneys had sought more time to decide on the timing of the testimony.
An NBC News/Wall Street Journal poll released Thursday found that 38% of respondents opposed Kavanaugh's nomination, marking the first time since the poll began in 2005 that more Americans opposed a Supreme Court nomination than supported it. The developments could also determine the fate of Kavanaugh's confirmation, which hangs on the votes of a handful of senators.