During a segment in which Schiff was invited on the show to promote a new book, Ortagus accused him of potentially helping to spread Russian disinformation through his promotion of the dossier and suggested his credibility had been diminished because of his actions.
"You defended, promoted and even read into the congressional record the Steele dossier. We know last week the main source of the dossier was indicted by the FBI for lying about most of the key claims in that dossier. Do you have any reflections on your role in promoting this to the American people?" Ortagus asked Schiff.
Schiff avoided directly answering the question, and instead called on "whoever lied" to former British intelligence officer Christopher Steele or the FBI to be prosecuted.
Igor Danchenko, the primary sub-source for the Steele dossier, was indicted last week as part of Special Counsel John Durham’s investigation into the origins of the probe into whether the Trump campaign colluded with Russia in the 2016 election.
Schiff attempted to change the subject to former President Donald Trump, criticizing him for pardoning individuals who had been convicted of lying to government officials during his administration, such as former National Security Advisor Michael Flynn and former campaign advisor Roger Stone.
Schiff noted that he pushed for the allegations in the dossier to be investigated when it first surfaced in 2017, but claimed there was no way for them to know if Steele had been given truthful information.
He tried to shift the attention to Trump once again, claiming that the investigation into the dossier unearthed that Trump campaign chairman Paul Manafort was sharing campaign polling data with Russian intelligence.
"And to be clear, he was fired halfway through the campaign," Ortagus said, interrupting Schiff's attempt to focus on Trump.
Schiff again tried to dodge the question and continue his claims of Russian collusion with the Trump campaign, however Ortagus interrupted him again.
"You may have helped spread Russian disinformation yourself for years by promoting this. I think that's what Republicans and what people who entrusted you as the intel committee chair are so confused about your culpability in all this," she said.
"I completely disagree with your premise. It’s one thing to say allegations should be investigated, and they were. It’s another to say that we should have foreseen in advance that some people were lying to Christopher Steele, which is impossible, of course, to do," Schiff said.
He claimed that the indictment of Danchenko shouldn't be used as a "smokescreen" to hide Trump's "culpability" when it came to colluding with Russia in 2016, Ukraine in 2020 and in "inciting an insurrection," referring to Jan. 6.
"None of that serious misconduct is in any way diminished by the fact that people lied to Christopher Steele," Schiff said.
"No I think just your credibility is," Ortagus shot back.
"I think the credibility of your question is in doubt," Schiff said.
Fox News' Brian Flood contributed to this report.