Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, called for an immediate postponement of Kavanaugh's confirmation proceedings in a letter to the committee's chairman, Iowa Republican Sen.
After the new allegations surfaced, Democrats called for a delay in Thursday's hearing.
"I can tell you that some women do not come forward because they fear not being believed, and a lot of other women don't come forward because of other women who make false accusations", Conway said. "This is a smear, plain and simple".
"This 35-year-old, uncorroborated claim is the latest in a coordinated smear campaign by the Democrats, created to tear down a good man", White House Spokesperson Kerri Kupec said.
Separately, Michael Avenatti, the lawyer best known for representing adult film star Stephanie Clifford, who says she had an affair with Donald Trump before he was elected president, said on Twitter that he represents a woman "with credible information regarding Judge Kavanaugh".
In a statement provided by the White House, Kavanaugh denies the event ever happened.
In addition, some of us knew Debbie long after Yale, and she never described this incident until Brett's Supreme Court nomination was pending.
Ramirez was initially hesitant to speak publicly, she told The New Yorker, partly because her memory contained gaps because she had been drinking at the time of the alleged incident. The magazine also reported that Ramirez spent six days "carefully assessing her memories and consulting with her attorney" before telling the full version of her story.
The latest allegation is that the nominee once exposed his genitals to a Yale University classmate at a party.
The classmate independently recalled numerous same details Ramirez told The New Yorker about the incident. "I don't think it was just 'Brett.' And I remember hearing and being mortified that this was out there".More news: Kavanaugh, Ford Agree to Testify on Thursday
The magazine said it has not confirmed with other eyewitnesses that Kavanaugh was present at the party at issue in Ramirez's account.
Ms Katz had called Mr Grassley's original deadline "arbitrary" and said its "sole goal is to bully Dr Ford and deprive her of the ability to make a considered decision that has life-altering implications for her and her family".
Trump, himself accused during the 2016 presidential race of sexual misconduct with numerous women, remained steadfast in his support for Kavanaugh.
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.
Senate Democrats are investigating the bombshell claim by Deborah Ramirez, according to the New Yorker magazine.
He said the "underhanded tactics" of the Democrats in the confirmation process, which he said included leaking allegations to the media, were not fair to Kavanaugh, "the individuals in the stories" or the public.
"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. "Neither she nor her legal representative have contacted the chairman's office".
Republicans, with a 51-49 Senate majority, can confirm Kavanaugh if they stay united.
Earlier on Saturday, a senior official at the White House said Ms Ford's requests amounted to "a clever way to push off the vote Monday without committing to appear Wednesday".
She says at one point, a plastic penis was pointed in her direction by one man, and later another exposed himself directly.