Updated at 5:43 p.m. ETSupreme Court nominee Judge Brett Kavanaugh says he isn't considering withdrawing in the wake of more allegations of sexual misconduct from decades ago."I'm not going to let false accusations drive us out of this process," Kavanaugh told Fox News' Martha MacCallum in an interview alongside his wife, Ashley, set to air Monday evening."We're looking for a fair process where I can be heard and defend my integrity and my lifelong record of promoting dignity and equality for women, starting with the women who knew me when I was 14 years old. I'm not going anywhere," Kavanaugh said in a clip released by Fox News prior to the planned broadcast.The new interview with Kavanaugh comes after new accusations surfaced Sunday night from Deborah Ramirez, who in a story published in The New Yorker alleges Kavanaugh exposed himself to her during a drunken party at Yale when both attended college there in the 1980s.This Thursday, the Senate Judiciary Committee has scheduled a hearing into the allegation by Christine Blasey Ford that Kavanaugh groped her and tried to remove her clothes during a party when both were in high school in Bethesda, Md., more than 30 years ago. Kavanaugh has denied the allegations leveled against him by both Ford and Ramirez.Ford and Kavanaugh have agreed to testify, although Sen. Dianne Feinstein, D-Calif., called for the panel to postpone the hearing following the allegation bu Ramirez.President Trump reiterated his support for Kavanaugh again on Monday, telling reporters on his way into the United Nations on Monday morning that Kavanaugh "is an outstanding person, and I am with him all the way."He said the charges "could be one of the single most unfair, unjust things to happen for a candidate for anything." The women making the allegations, Trump said, "were coming out of the woodwork and, he said, "in my opinion totally political."And in a tweet to his more than 50 million followers Monday evening Trump touted the Fox News interview and added " This is an outstanding family who must be treated fairly!"The latest accusation comes from Deborah Ramirez, who in a story published in The New Yorker alleges Kavanaugh exposed himself to her during a drunken party at Yale when both attended college there in the 1980s.In a letter to the Senate Judiciary Committee released earlier Monday, Kavanaugh called the accusations attempts at "last minute character assassination":