A lawyer for the second woman who publicly accused Supreme Court nominee Brett Kavanaugh of sexual misconduct said Tuesday night that the FBI must investigate the accusations of his client, Deborah Ramirez.

John Clune, speaking to CNN's Anderson Cooper, said the accusations put forth by Ramirez have to be investigated by law enforcement officials, rather than lawmakers on the Senate Judiciary Committee.

"This has to be investigated by meaningful law enforcement. This is not something that can be done by the Senate," Clune said. "This has to be done by FBI who can investigate the matter with the threat of perjury. Our client's willing to do that."

Ramirez, in a piece published by The New Yorker on Sunday, claimed that Kavanaugh exposed himself to her at a party while they were students at Yale University 35 years ago — an allegation that the judge has denied and called a "smear."

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Her accusation came days after Dr. Christine Blasey Ford said the judge sexually assaulted her when they were teenagers.

Cooper addressed concerns about Ramirez's allegations, specifically that it took Ramirez — as noted in the article — "six days of carefully assessing her memories and consulting with her attorney" before she felt comfortable coming foward to name Kavanaugh.

Clune said that while he was not representing Ramirez at that time, he's come to know her as "very, very careful and very deliberate" in her effort to accurately recall the situations she claims happened in college.

Ramirez wanted to "make sure that what she was actually going to be disclosing publicly was information that she could rely on, and that she could stand by, and that was accurate" — telling Cooper that Ramirez is "probably the most careful and conscientious client that I've ever represented."

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"She is very adamant that she's not going to put forward information that she doesn't actually recall and doesn't think it's something she can rely on," Clune said. Claims that Ramirez consulted with other people to clarify her recollections, Clune argued, "was just smart investigation to make sure that she wasn't remembering things inaccurately or by the passage of time."

Earlier on Twitter, Clune said Ramirez wants to give a sworn statement to the FBI regarding her allegations, and said that the Senate Judiciary Committee has so far "refused to meet all scheduled appointments."

He said that during a previously scheduled phone call with the committee, only Democrats showed up for the call, while Republicans did not.

"We have officially requested an FBI investigation and our client remains adamant that is the appropriate venue for her to discuss her trauma," Clune tweeted.

Kavanaugh and Ford are scheduled to testify in front of the committee on Thursday, and on Friday, a tentatively rescheduled vote on Kavanaugh's nomination is set to take place.

The Associated Press contributed to this report.