Neither allegation has been corroborated, and Kavanaugh has issued strong denials to both.
Senator Orrin Hatch, a Republican member of the committee, blamed Democrats for the new allegation.
He said he "did not have sexual intercourse or anything close to sexual intercourse in high school or for many years thereafter".
The New Yorker magazine reported Sunday night that Senate Democrats were investigating a second woman's accusation of sexual misconduct by Kavanaugh dating to the 1983-84 academic year, Kavanaugh's first at Yale University.
Kavanaugh sent the letter today, a day after the New Yorker published allegations from former fellow Yale student Deborah Ramirez that the judge exposed himself to her at a party in college.
White House spokesperson Kerri Kupec dismissed Ramirez´s allegation as "the latest in a coordinated smear campaign by the Democrats created to tear down a good man".
Sen. Dianne Feinstein of California, the ranking Democrat on the Judiciary Committee, called for the "immediate postponement" of any further action on Kavanaugh's nomination.
The New Yorker said it contacted Ramirez after learning of a possible involvement in an incident with Kavanaugh. So far, no Republican senators have said they would vote against him. The Democrats then began investigating.
"In her initial conversations with The New Yorker, she was reluctant to characterize Kavanaugh's role in the alleged incident with certainty", wrote New Yorker writers Ronan Farrow and Jane Mayer.
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"After six days of carefully assessing her memories and consulting with her attorney, Ramirez said that she felt confident enough of her recollections..." Ramirez and her attorney could not be reached for comment on the record. Ford has said Kavanaugh tried removing her clothes and covered her mouth to prevent screams after he pinned her on a bed during a high school party.
The president also criticized the accusers, saying they took decades to come forward.
The magazine said it had not found eyewitnesses to confirm that Kavanaugh was at the party, though one former classmate remembered hearing about the incident from another, and independently corroborated numerous details offered by Ramirez. And he noticed a vote on Kavanaugh's nomination for Friday morning before the Judiciary Committee.
Kavanaugh has strongly denied the claim, and now, it looks like the judge is ready to fight.
With increasing intensity, Republicans have attacked the credibility of Ford's and now Ramirez' accounts. As I've noted, we know the chain of custody of the letter went through the Democratic side of the Judiciary Committee. In addition, some of us knew Debbie long after Yale, and she never described this incident until Brett's Supreme Court nomination was pending.
But who will be asking the questions remains unresolved, the lawyers said.
It is notable that in the context of these parties, friends are named and these friends are "other than those identified by Dr. Blasey".
The new information came hours after the Senate committee agreed to a date and time for a hearing after almost a week of uncertainty over whether Ford would appear to tell her story.
Linda Sarsour signals for quiet as activists opposed to President Donald Trump's embattled Supreme Court nominee, Brett Kavanaugh, demonstrate before being arrested, on Capitol Hill in Washington, Monday, Sept. 24, 2018. A spokesman for the committee's chairman, Senator Chuck Grassley, R-Iowa, confirmed that the hearing would take place at 10 a.m. on Thursday.