In July, as President Trump was preparing a prime-time speech on election security, word went out from executives at Fox News: The network would avoid covering his stock claims about a stolen election.

Fox had landed in serious legal trouble in 2021 after amplifying false assertions by Mr. Trump’s allies about vote-stealing election machines, culminating in an extraordinary $787 million defamation settlement.

In 2020, Fox Business host Maria Bartiromo had made her show a central stop for proponents of the president’s election theories. And this summer, too, she was preparing to interview the presidential adviser Peter Navarro the morning after the speech.

But after she received a text message written by a Fox Business executive warning against post-speech coverage, she canceled Mr. Navarro’s appearance.

As she did so, she shared the executive’s text with Mr. Navarro, who promptly sent it “up the chain” to the White House, he said in an interview Friday. It was his duty, he said, to relay “yet another example of Fox personnel censoring the Trump administration.”

That sequence of events, described by Mr. Navarro and two other sources familiar with the discussions, would bring an abrupt end to Ms. Bartiromo’s on-air career at the network. The White House complained to Fox, which saw the disclosure of the communication as a breach of company policy. Fox News did not provide a comment.

A lawyer for Ms. Bartiromo, Bryan Freedman, called her “one of the hardest-working journalists throughout her award-winning career.”

Ms. Bartiromo’s cancellation was a dramatic split between the nation’s most-watched cable news channel and one of cable’s earlier, defining stars.

But it also revealed an important shift at the network in the years since the 2020 election — one that could have real consequences for Mr. Trump as he seeks to again assert the American election system is rife with fraud before a midterm election that, polling shows, could be rough for his party.

Where in 2020 he could count on hosts like Ms. Bartiromo to air his wildest election claims on Fox’s top-rated programs without much pushback, he cannot do so now.

The changes are a consequence of the legal straits the network found itself in after the election, when two voting technology companies at the heart of the stolen election theories, Dominion Voting Systems and Smartmatic, sued Fox for $1.6 billion and $2.7 billion, respectively, for tarnishing their reputations.

The $787.5 million settlement stemmed from the Dominion case; its litigation with Smartmatic is ongoing, adding to the incentives to be careful about promoting conspiracies this election year.

Fox is in some ways a different network than it was in late 2020, in front of the camera and behind the scenes.

The chief Fox legal officer Viet Dinh, whose handling of the Dominion case came under question, is no longer there. Neither is a Dinh deputy and former Trump aide, Raj Shah, who helped keep the network hyper-focused on right-wing criticism when it or its hosts were viewed as being insufficiently deferential to Mr. Trump’s fraud claims after the election.

Early in 2021, Fox ended the program of the host Lou Dobbs, who had been among the more enthusiastic promoters of claims the presidential election was rigged. After the Dominion settlement, it parted ways with its host Tucker Carlson, who was mentioned in the case but also drew advertiser boycotts with his hard dive into right-wing conspiracies.

Another figure in the two voting cases, Jeanine Pirro, is now working as Mr. Trump’s U.S. attorney for the District of Columbia.

Fox’s most popular hosts remain overwhelmingly loyal to Mr. Trump, including its prime-time stars, Sean Hannity, Laura Ingraham and Jesse Watters, and the network still tilts heavily in his favor.

But it has also shown a willingness to break from the administration on, for instance, its military campaign in Iran, which has been criticized by some on-air hosts, including Ms. Ingraham. The anchor Bret Baier delivered a rare, on-air defense of his colleague, Jonathan Hunt, when Mr. Trump blasted his coverage of Iran.

In the interview on Friday, Mr. Navarro, who formally serves as Mr. Trump’s senior counselor on trade, shared his displeasure with the shift. He said the network could not be trusted to “tell the truth about certain topics.”

He had no such issues with Ms. Bartiromo, whose approach — at times permitting guest commentators to free-associate on live television — had not appeared to change much in the years since the Dominion settlement. Puck, a news website, earlier reported on Ms. Bartiromo’s conversations with Mr. Navarro.

That was clear in July, when the network was sued for defamation after Kevin O’Leary, the investor of “Shark Tank” fame, used Ms. Bartiromo’s show to settle a score with his detractors. He baselessly claimed that two nonprofit founders in Utah who were opposing his plans for a 40,000-acre data center near the Great Salt Lake were Chinese agents.

According to the lawsuit, Ms. Bartiromo not only failed to challenge Mr. O’Leary, she “legitimized” his accusation.

The network’s response afterward was more reflective of the post-Dominion shift. Whereas the network stonewalled Dominion when it initially complained about its election-fraud coverage, it moved more quickly to apologize after Mr. O’Leary retracted his claims.

Ms. Bartiromo still has considerable time left on her contract, according to two people familiar with the matter, meaning that Fox News is still obligated to pay her millions a year despite ending her on-air role. The contract could also keep her from appearing on other networks.

Mr. Trump, who called Ms. Bartiromo a “total professional, and a true warrior” in a Truth Social post on Thursday, added that her “fans, of which there are many, will not be happy.”