Grassley, an Iowa Republican, told reporters Wednesday that while they are investigating the new allegation, there will not be a delay of the prescheduled hearing, saying "tomorrow is very important".
He and one of the accusers, Christine Blasey Ford, will testify publicly Thursday before the Judiciary Committee.
Avenatti also represents porn star Stormy Daniel's in her defamation lawsuit against President Donald Trump.
In her affidavit, Swetnick says she met Kavanaugh at a house party and continued to see him at parties, which she said were a near-weekly occurrence during the school years of 1981 to 1983. Only 12 percent of Democrats agreed that senators should confirm Kavanaugh if he sexually assaulted Dr. Christine Blasey Ford when both were in high school.
Lawyer Michael Avenatti provided a statement from his client to the committee. She alleges a decades-old sexual assault by Kavanaugh. Asked about the decision to have a veteran Arizona prosecutor to handle the questioning, Trump said that Senate Republicans "could not be nicer" and "could not be more respectful".More news: Google quietly started logging people into Chrome without their consent
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He added, "I strongly believe Judge Kavanaugh should withdraw from consideration".
Kavanaugh and the other three named people: Mark Judge, Patrick Smyth, and Leland Keyser, have all given personal testimony.
Clune told Davis that Ramirez wants an FBI investigation and would agree to be interviewed by the committee "on appropriate terms".
"The Republicans could not be nicer, could not be more respectful to the process. But I have never done that to her or to anyone", he will say on Thursday as per the prepared testimony.
Swetnick's statement does not claim sexual assault, but it does say she saw Kavanaugh at parties "engage in abusive and physically aggressive behavior toward girls" and spike the punch with alcohol.