Michael Avenatti, lawyer of adult-film actress Stormy Daniels, arrives at federal court in New York, U.S., on Wednesday, May 30, 2018.

On Sunday, the attorney — who represents porn star Stormy Daniels in her lawsuit against President Donald Trump — claimed he represents a woman "with credible information" regarding Kavanaugh and friend Mark Judge. Mike Davis, chief counsel for nominations for the Senate Judiciary Committee, emailed him requesting the information, according to a message Avenatti publicly shared.

The Senate Judiciary Committee contacted Michael Avenatti after the lawyer claimed to represent a client who has damaging information about Supreme Court nominee Brett Kavanaugh.

Avenatti responded that he and his client would provide "additional evidence" related to explosive allegations of misconduct "in the coming days." It is unclear what evidence the lawyer has. On Monday, Avenatti told CNBC that his client will make claims about Kavanaugh public in an interview in the next two days. Avenatti said he could not yet identify where that interview will appear.

Taylor Foy, a spokesman for Judiciary Committee Chairman Chuck Grassley, R-Iowa, confirmed the exchange was genuine. The panel's staff "requested that Mr. Avenatti provide any evidence that he claims to have," Foy said.

A White House spokesman who oversees Kavanaugh's confirmation did not immediately respond to a request to comment on the lawyer's accusations.

Avenatti, a frequent and vocal Trump critic, has said he is considering running for president as a Democrat in 2020.

Avenatti's claims came as a second woman accused Kavanaugh of sexual misconduct. In a New Yorker story published Sunday, the judge's college classmate, Deborah Ramirez, says he exposed himself to her at a Yale University party in the early 1980s. Kavanaugh called the allegation a "smear" and said that "this alleged event from 35 years ago did not happen."