WASHINGTON - Hours after his Supreme Court pick was sworn in Saturday, President Donald Trump said on Fox News that those who made up "false" stories about Brett Kavanaugh should be penalized.

Trump, talking with Fox News' Jeanine Pirro, said he hated watching the slew of sexual assault allegations grow against Kavanaugh and dubbed all the accusations "fabrications" with "not a bit of truth."

"I think that they should be held liable," Trump told Pirro. "You can't go around and whether it's making up stories or making false statements about such an important position, you can't do that. You can destroy somebody's life."

Pirro started the segment by congratulating the president on Kavanaugh's swearing-in then asked about the accusations and whether any of those who came forward or promoted "falsehoods" should suffer "consequences." She specifically asked about allegations brought by Julie Sweatnick, who was represented by lawyer Michael Avenatti.

Swetnick alleges she witnessed efforts by Kavanaugh and his classmate Mark Judge to get teenage girls "inebriated and disoriented so they could then be 'gang-raped' in a side room or bedroom by a 'train' of numerous boys."

Avenatti has been dueling with the president for months in court representing porn star Stormy Daniels, who alleges an affair with Trump and signed a hush money deal to stay quiet.

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Trump alleged Avenatti had made "false accusations about me" in the past and said he would love to see libel laws get tougher.

Trump said he watched the saga and watched Kavanaugh suffer "with false statements made about him, things that never happened."

"There were many, many false things that were said about a very, very fine man and would have destroyed his family if this didn't happen," Trump said, referring to the confirmation. "It all came together in the end and people realized it was false accusations and false statements."

Avenatti, in an interview with USA TODAY, said it was despicable that Trump and others, including members of the media, would call his client's claims false without first investigating them. Swetnick was not interviewed by the FBI in its investigation of Kavanaugh.

"Donald Trump is the most dishonest individual to ever hold the office of President of the United States," Avenatti said. "He is the last person in the nation that should be accusing other people of engaging in falsehoods."

He added his client was "trying to hold it together" after Saturday's vote but was "disgusted" by the barrage of attacks. "This is why women don't report sexual assaults," he said.

Earlier Saturday, Trump praised Senate Republicans for their work in getting Kavanaugh confirmed and said he believes a speech he made earlier this week attacking the credibility of accuser Christine Blasey Ford helped generate support for the embattled nominee.

“I think that the Mississippi speech had a great impact, yes - I think it was a very important thing," Trump told reporters aboard Air Force One en route to a political rally in Topeka, Kansas.

During the controversial speech, Trump mocked Ford and mimicked her, claiming her allegations against Kavanaugh lacked sufficient detail. Numerous lawmakers, including undecided Republican senators like Susan Collins and Jeff Flake, said they were appalled by Trump's behavior, but wound up voting for Kavanaugh anyway.

Contributing: David Jackson