Former acting FBI director Andrew McCabe claimed Thursday there is an "inherent weakness" in the process the FBI uses to obtain warrants under the Foreign Intelligence Surveillance Act and expressed doubt that it will be corrected without any major change.

During a rare public appearance, McCabe -- a controversial figure who was fired in 2018 over allegations he gave false statements to federal agents and has since sued the DOJ over his termination -- also insisted political bias played no role in the Trump-Russia probe.

But when discussing FISA warrants, McCabe pointed to how the review used to verify information in FISA applications -- known as the Woods procedures -- fails to address the first step in the process, which is when an FBI case agent determines whether the information is relevant enough to pass along.

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“Where things fall apart is where they don’t see things as necessarily mitigating,” McCabe said during a panel discussion on the FISA process at NYU Law School Thursday.

McCabe, a CNN analyst who has been a target of Republicans for his role in the Hillary Clinton and Trump-Russia probes, explained that this fundamental decision-making by agents is not taken into account by the Woods procedures, and because the case agent is the only one with knowledge of this information, nothing can be done about it. He said this is an “inherent weakness in the process that we’re never going to fix” unless other people are able to know everything the case agents know.

Former FBI official Andrew McCabe during a panel discussion on the FISA process at NYU Law School Thursday. (Ronn Blitzer/Fox News).

McCabe said that in all his years with the FBI, every time he had been in a meeting about whether to disclose information, it ended with the decision to disclose it.

“My concern is for the issues that don’t find their way to a meeting,” he said.

This was the crux of McCabe’s problems with the FISA process in the wake of Justice Department Inspector General Michael Horowitz’s lengthy report on the FBI’s failures in using FISA to conduct surveillance of former Trump campaign adviser Carter Page. Horowitz found that there were 17 instances of errors or omissions in the warrant application and subsequent renewals, including a doctored email chain.

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Horowitz concluded that there was no documentary or testimonial evidence that the Russia investigation – of which the Page FISA warrant was a part – was launched based on any political bias, although he said the issue “gets murkier” when it comes to the FISA process.

McCabe denied that there is any chance political bias played a role in the Russia probe, despite claims from President Trump and his supporters. Trump has repeatedly attacked McCabe and raised questions about his wife's past Democratic political activities and connections.

“No, there is no truth to that,” McCabe said, although he recognized that Horowitz “didn’t like the answers he got” in terms of reasons for the FISA failures.

McCabe’s own involvement in the Clinton email case has also come under scrutiny. Trump himself has suggested McCabe was in the tank for the Clintons, drawing attention to how McCabe’s wife, Jill McCabe, received donations from Virginia Gov. Terry McAuliffe's super PAC while she ran for a state Senate seat in Virginia in 2015. McAuliffe is a close Clinton ally. McCabe did not recuse himself from the Clinton investigation until a week before the election.

McCabe on Thursday acknowledged that it is possible that individuals could have inherent cultural biases but said he never saw “the introduction of political bias to the work that we do.”

After Horowitz released his report, Democrats defending the Russia investigation pointed to the lack of a determination of political bias as evidence that Trump's campaign was not being unfairly targeted.

Sen. Rand Paul, R-Ky., indicated that this would be a flawed assumption during a Senate Homeland Security and Governmental Affairs Committee hearing in December, questioning whether Horowitz's inability to find evidence of bias really meant that there had not been any bias.

"Just because you didn’t find it doesn’t mean it didn’t exist,” Paul said, noting that there could have been 15 people involved whose bias influenced their decisions, but it just wasn’t provable.

"We could not prove it. We lay out here what we can," Horowitz replied.

Andrew Weissmann, a senior prosecutor with then-special counsel Robert Mueller’s office, was part of the same panel alongside McCabe, and echoed McCabe’s assertion that politics did not play a role, noting that the FBI only has one political appointee in the director, while agents are “apolitical and dedicated.” Mueller's office took over the Russia probe from the FBI soon after Trump fired FBI Director James Comey.

Weissmann also addressed the proposed FISA reforms put forth by FBI director Christopher Wray, which were deemed “insufficient by David Kris, who was appointed by the Foreign Intelligence Surveillance Court (FISC) to oversee the suggested reforms. Kris told the court Wednesday that the FBI’s proposals must be “expanded dramatically.”

Those expansions, according to Kris, should address issues including the “need to improve cooperation between the FBI and DOJ attorneys.”

Indeed, the FISC "should require the FBI and DOJ to document and report on the nature and extent of this communication; such a requirement to document and report communication may encourage the FBI and DOJ to conduct more of it," he said. Every time Wray "visits a field office in 2020," Kris wrote, he should stress the importance of accuracy in FISA applications.

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Weissmann agreed with Kris that Wray’s proposals were lacking but said even Kris’ suggestions were not sufficient.

“I think that David is a really great lawyer,” Weissmann said, but added, “I was a little disappointed. I didn’t think it went far enough.”

Fox News’ Gregg Re and Jake Gibson contributed to this report.