Former President Donald Trump's final chief of staff in the White House, Mark Meadows, has spoken with special counsel Jack Smith's team at least three times this year, including once before a federal grand jury, which came only after Smith granted Meadows immunity to testify under oath, according to sources familiar with the matter.

The sources said Meadows informed Smith's team that he repeatedly told Trump in the weeks after the 2020 presidential election that the allegations of significant voting fraud coming to them were baseless, a striking break from Trump's prolific rhetoric regarding the election.

According to the sources, Meadows also told the federal investigators Trump was being "dishonest" with the public when he first claimed to have won the election only hours after polls closed on Nov. 3, 2020, before final results were in.

"Obviously we didn't win," a source quoted Meadows as telling Smith's team in hindsight.

Trump has called Meadows, one of the former president's closest and highest-ranking aides in the White House, a "special friend" and "a great chief of staff -- as good as it gets."

The descriptions of what Meadows allegedly told investigators shed further light on the evidence Smith's team has amassed as it prosecutes Trump for allegedly trying to unlawfully retain power and "spread lies" about the 2020 election. The descriptions also expose how far Trump loyalists like Meadows have gone to support and defend Trump.

Sources told ABC News that Smith's investigators were keenly interested in questioning Meadows about election-related conversations he had with Trump during his final months in office, and whether Meadows actually believed some of the claims he included in a book he published after Trump left office -- a book that promised to "correct the record" on Trump.

ABC News has identified several assertions in the book that appear to be contradicted by what Meadows allegedly told investigators behind closed doors.

According to Meadows' book, the election was "stolen" and "rigged" with help from "allies in the liberal media," who ignored "actual evidence of fraud, right there in plain sight for anyone to access and analyze."

But, as described to ABC News, Meadows privately told Smith's investigators that -- to this day -- he has yet to see any evidence of fraud that would have kept now-president Joe Biden from the White House, and he told them he agrees with a government assessment at the time that the 2020 presidential election was the most secure election in U.S. history.

'We did win this election'

Trump was already questioning the integrity of the election months before Election Day. Then, within hours of polls closing on Nov. 3, 2020 -- as Trump was beginning to lose key states -- Trump claimed on national TV that it was all "a major fraud."

"Frankly, we did win this election," Trump declared.

Meadows told investigators earlier this year that he's long believed Trump was being dishonest when he made that statement, given the fact that votes were still being counted and the results from several states were not in yet.

Nevertheless, public testimony has shown that in the weeks after the election, Meadows helped Trump vet allegations of fraud that were making their way to Trump from people like Rudy Giuliani, whom Trump put in charge of legal efforts to keep Trump in the White House.

But Meadows said that by mid-December, he privately informed Trump that Giuliani hadn't produced any evidence to back up the many allegations he was making, sources said. Then-attorney general Bill Barr also informed Trump and Meadows in an Oval Office meeting that allegations of election fraud were "not panning out," as Barr recounted in testimony to Congress last year.

Meadows has said publicly that he believed "a number of allegations" still warranted "further investigation," and that he "hadn't reached a conclusion" on the election overall by late December.

Also by then, Trump had run out of legal options. When the U.S. Supreme Court on Dec. 11, 2020, denied his final court challenge, Trump told Meadows something to the effect of, "Then that's the end," or, "So that's it," Meadows recalled to investigators, according to sources.

Still, Trump wouldn't back down, insisting there was widespread fraud but that the Justice Department wasn't "looking for it," Barr recalled.

While speaking with investigators, Meadows was specifically asked if Trump ever acknowledged to him that he'd lost the election. Meadows told investigators he never heard Trump say that, according to sources.

On Jan. 2, 2021, Meadows helped set up the now-infamous phone call between Trump and Georgia Secretary of State Brad Raffensberger, during which Trump pressed Raffensberger to "find 11,780 votes ... because we won the state."

Meadows has said publicly that he essentially introduced everyone on the call -- which is corroborated by transcripts of the call that were made public -- and he has said he was simply trying to help them resolve a dispute over Georgia's election results.

On the call, Trump mentioned allegations of fraudulent ballots hidden in suitcases, which the Justice Department had already taken "a hard look at" and debunked, according to Barr's testimony.

As described to ABC News, Meadows told Smith's investigators that, around that time, there were many times he wanted to resign over concerns that the way certain allegations of fraud were being handled could have a negative impact -- but he ultimately didn't leave because he wanted to help ensure a peaceful transfer of power.

'Sheer volume of falsehoods'

Aided by a ghostwriter, Meadows published his book, "The Chief's Chief," nearly a year after Trump left office.

"[T]he sheer volume of falsehoods that have been published about the president's time in the White House is astounding," the book says. "I consider this book a small opportunity to correct the record."

Trump even promoted the book himself, issuing a statement in December 2021 saying the book "rightfully spends much time talking about the large-scale Election Fraud that took place ... also known as the Crime of the Century."

But sources told ABC News that when speaking with Smith's investigators, Meadows conceded that he doesn't actually believe some of the statements in his book.

According to the sources, Meadows told investigators that he doesn't agree with what's in his book when it says "our many referrals to the Department of Justice were not seriously investigated."

Meadows told investigators he believes the Justice Department was taking allegations of fraud seriously, properly investigating them, and doing all they could to find legitimate cases of fraud -- and he told investigators he relayed all that to Trump a few weeks after the election, the sources said.

Similarly -- as described by sources to ABC News -- despite Meadows telling investigators that Giuliani never produced evidence of significant fraud in the election, his book refers to Giuliani's efforts to expose "the fraud, and the dirty tricks on election night."

"The people who rigged this election knew that eventually, these irregularities would come to light ... [So] they conducted the operation, then attacked anyone who dared ask questions about what they had done," his book says.

Meadows went even further while promoting his book on right-wing media in November 2021. When asked by a podcast host if he believes the outcome of the 2020 election was fraudulent, Meadows responded, "I do believe that there are a number of fraudulent states ... I've seen at least illegal activity in Pennsylvania [and] in Georgia" -- referring to two key states that clinched the White House for Biden.

Under the penalty of perjury, Meadows offered a vastly different assessment to Smith's investigators, telling them he's never seen any evidence of fraud that would undermine the election's outcome, according to what sources told ABC News.

'I guess these people are more upset'

The final report by the U.S. House committee investigating the Jan. 6, 2021, attacks on the U.S. Capitol accused Meadows of including "a number of intentional falsehoods" in his book, but the committee's report focused on allegations about Trump's actions on that fateful day, not claims about the election more broadly.

Portions of what Meadows told investigators appear to align with broader testimony that other top White House aides, including former Meadows assistant Cassidy Hutchinson, provided to the House committee, describing a president seemingly hesitant to take decisive action to stop the violent mob on Jan. 6, 2021.

Sources said Meadows confirmed that at one point, as the riots were unfolding, Trump got on a call with then-House Republican leader Kevin McCarthy, and told McCarthy, "I guess these people are more upset than you are."

However, according to what Meadows told investigators, Trump seemed to grow increasingly concerned as he learned more about what was transpiring at the Capitol, and Trump was visibly shaken when he heard that someone had been shot there, sources said.

Trump supporter Ashli Babbitt was fatally shot when she tried to break through a barricaded entrance near the House chamber. Other Trump supporters sustained fatal injuries that day, and a law enforcement officer died after trying to defend the Capitol.

Meadows has not been charged in Smith's federal case, he has been charged -- along with Trump, Giuliani and 16 others -- by authorities in Georgia for allegedly trying to overturn the election results in that state. Four of those charged have already pleaded guilty and agreed to testify for the prosecution, while the others, including Meadows, Trump and Giuliani, have pleaded not guilty and are awaiting trial.

Meadows sought to have the Georgia case against him moved to federal court, but that effort was denied. He is now appealing that decision.

From 2013 to 2020, Meadows represented North Carolina in Congress, where he also led the conservative House Freedom Caucus for two years.

Under the immunity order from Smith's team, the information Meadows provided to the grand jury earlier this year can't be used against him in a federal prosecution.

Trump has pleaded not guilty in the election-related federal case against him.

A spokesperson for Smith and an attorney for Meadows declined to comment to ABC News for this story. A spokesperson for Trump's presidential campaign did not immediately respond to a request for comment.