Sen. Bill Cassidy (R., La.) tweeted on Tuesday that a "criminal referral should be sent to the FBI" after Julie Swetnick backtracked on some allegations she levied against Supreme Court nominee Brett Kavanaugh in a sworn statement.

Swetnick's attorney, Michael Avenatti, provided the Senate with her sworn statement in which she alleged Kavanaugh was complicit in "gang rape" parties in the 1980s. Swetnick, however, appeared to backtrack on some of her initial claims in an interview with NBC on Monday night.

"A criminal referral should be sent to the FBI/DOJ regarding the apparently false affidavit signed by Julie Swetnick that was submitted to the Senate by @MichaelAvenatti," Cassidy tweeted.

A criminal referral should be sent to the FBI/DOJ regarding the apparently false affidavit signed by Julie Swetnick that was submitted to the Senate by @MichaelAvenatti. — U.S. Senator Bill Cassidy, M.D. (@SenBillCassidy) October 2, 2018

In her sworn affidavit, Swetnick said in the early 1980s she attended multiple parties where she saw Kavanaugh–then in high school–"engage in abusive and physically aggressive behavior toward girls," "grind" on girls,"drink excessively," and "spike" the "punch" with alcohol or drugs in an effort to make girls lose their inhibitions. She claimed that at these parties, men–including Kavanaugh–would line up outside of a bedroom to rape drunk girls. Swetnick said she was gang raped at one of these parties, though she did not claim Kavanaugh raped her.

On Monday, she appeared less certain of Kavanaugh's role in her allegations, saying, "I don't know what [Kavanaugh] did, but I saw him by [punch containers]." She said she "didn't know what was occurring" in the bedrooms she initially described as the site of gang rapes, but said it was "just too coincidental" that wasn't what was happening.

The FBI is investigating some of the claims made against Kavanaugh by women such as Christine Blasey Ford and Deborah Ramirez, at the request of President Donald Trump and the Senate Judiciary Committee. Following a call to do so by Sen. Jeff Flake (R., Ariz.) on Friday, Trump authorized a "limited" background investigation into the allegations, to be completed this week.

Kavanaugh has denied all the allegations against him, calling them "last minute smears" in an attempt to stall his confirmation.

Avenatti has called for the FBI to investigate the claims made by his client, but it has not yet been confirmed that Swetnick is being interviewed.

"How do you conduct a legitimate, fair & thorough investigation into allegations unless you interview the person actually making the allegations about her experiences, what she witnessed, and what facts and other witnesses she is aware of?" Avenatti asked on Twitter on Sunday. "Answer – YOU CAN’T. And that’s by design."

How do you conduct a legitimate, fair & thorough investigation into allegations unless you interview the person actually making the allegations about her experiences, what she witnessed, and what facts and other witnesses she is aware of? Answer – YOU CAN’T. And that’s by design. — Michael Avenatti (@MichaelAvenatti) September 30, 2018

Trump has denied influencing the FBI investigation and limiting their witness list, saying in a tweet on Saturday, "I want them to interview whoever they deem appropriate, at their discretion."

Avenatti, who also represents Stormy Daniels, the adult film actress who filed a defamation suit against Trump, has a contentious history with the president. Trump has referred to Avenatti as a "low-life" and a "third rate lawyer."

In a list published by Senate Majority Leader Mitch McConell (R., KY) on Sunday, he laid out allegations that undermine Swetnick's credibility, including a defamation suit filed against her related to sexual misconduct charges, a restraining order filed against her by an ex-boyfriend, lying to an employer about having attended Johns Hopkins University, and two tax liens.

Speaking to reporters Tuesday afternoon about Kavanaugh's confirmation and the allegations made against him, Trump said, "I don't think you should lie to Congress."