WILMINGTON, Delaware — Fox and Dominion Voting Systems reached a $787 million settlement Tuesday in the voting machine company’s defamation lawsuit, averting a trial in a case that exposed how the top-rated network chased viewers by promoting falsehoods about the 2020 presidential election.

“The truth matters. Lies have consequences,” a Dominion lawyer, Justin Nelson, said in a news conference outside the courthouse after a judge announced the deal.

Dominion had asked for $1.6 billion in arguing that Fox had damaged its reputation by helping peddle conspiracy theories about its equipment switching votes to President Biden from President Trump. Fox said the amount greatly overstated the value of the Colorado-based company.

The resolution in Delaware Superior Court follows a recent ruling by Judge Eric Davis in which he allowed the case to go to trial while emphasizing it was “CRYSTAL clear” that none of the allegations about Dominion aired on Fox by Trump allies were true.

In a statement issued shortly after the announcement, Fox News said the network acknowledged “the court’s rulings finding certain claims about Dominion to be false.” It did not respond to an inquiry asking for elaboration.

Inquiries to Dominion and Fox were not immediately returned.

Records released as part of the lawsuit showed how Fox hosts and executives did not believe the claims by Mr. Trump’s allies but aired them anyway, in part to win back viewers who were fleeing the network after it correctly called hotly contested Arizona for Mr. Biden on election night.

The settlement, if formally accepted by the judge, will end a case that has proven a major embarrassment for Fox News. If the case had gone to trial, it also would have presented one of the sternest tests to a libel standard that has protected media organizations for more than half a century.

Several First Amendment experts had said Dominion’s case was among the strongest they had ever seen. Still, there was real doubt about whether Dominion would be able to prove to a jury that people in a decision-making capacity at Fox could be held responsible for the network’s airing of the falsehoods.

Dominion accused Fox of defaming it by repeatedly airing, in the weeks after the 2020 presidential election, false allegations by Trump allies that its machines and the software they used had flipped votes to Mr. Biden — even as many at the network doubted the claims and disparaged those who were making them.

The company sued both Fox News and its parent, Fox Corporation, and said its business had been significantly damaged.

During a deposition, Fox’s chairman, Rupert Murdoch, who founded the network, testified that he believed the 2020 election was fair and had not been stolen from Trump.

“Fox knew the truth,” Dominion argued in court papers. “It knew the allegations against Dominion were ‘outlandish’ and ‘crazy’ and ‘ludicrous’ and ‘nuts.’ Yet it used the power and influence of its platform to promote that false story.”

In his March 31 summary judgment ruling, Judge Davis pointedly called out the news organization for airing falsehoods while noting how the bogus election claims persist, 2 1/2 years after Mr. Trump lost his bid for reelection.

“The statements at issue were dramatically different than the truth,” Judge Davis said in that ruling. “In fact, although it cannot be attributed directly to Fox’s statements, it is noteworthy that some Americans still believe the election was rigged.”

In its defense, Fox said it was obligated to report on the most newsworthy of stories — a president claiming that he had been cheated out of reelection.

“We never reported those to be true,” a Fox lawyer, Erin Murphy, said. “All we ever did was provide viewers the true fact that these were allegations that were being made.”

Fox said Dominion had argued that the network was obligated to suppress the allegations or denounce them as false.

“Freedom of speech and of the press would be illusory if the prevailing side in a public controversy could sue the press for giving a forum to the losing side,” Fox said in court papers.

In a 1964 case involving The New York Times, the Supreme Court limited the ability of public figures to sue for defamation. The court ruled that plaintiffs needed to prove that news outlets published or aired false material with “actual malice” — knowing such material was false or acting with a “reckless disregard” for whether or not it was true.

That has provided news organizations with stout protection against libel judgments. Yet the nearly six-decade legal standard has come under attack by some conservatives in recent years, including Mr. Trump and Governor DeSantis of Florida, who have argued for making it easier to win a libel case.

Two Republican-nominated Supreme Court justices, Clarence Thomas and Neil Gorsuch, have publicly expressed interest in revisiting the protection.

Dominion’s lawyers argued that Fox made a deliberate decision to repeatedly air the false claims to appeal to viewers. 

They allowed guests to claim that the company had rigged the election, flipped large numbers of votes to Mr. Biden through a secret algorithm, was owned by a company founded in Venezuela to rig elections for its late president, Hugo Chavez, and bribed government officials.

“What they did to get viewers back was start this new narrative that the election had been stolen and that Dominion was the thief,” a Dominion lawyer, Rodney Smolla, said during a March hearing.

A mountain of evidence — released in the form of deposition transcripts, internal memos and emails from the time — was damaging to Fox even if some of it was only tangentially related to the libel argument.

Dominion has pointed to text and email messages in which Fox insiders discounted and sometimes overtly mocked the vote manipulation claims. One Fox vice president called them “MIND BLOWINGLY NUTS.”

Much of the material showed a network effectively terrified of its audience after its election night declaration that Mr. Biden had won Arizona. The race call infuriated Mr. Trump and many viewers who supported him.

One of Fox’s top news anchors, Bret Baier, noted the audience’s anger and suggested rescinding the call, even awarding the state to Mr. Trump.

“We don’t want to antagonize Trump further,” Mr. Murdoch said in a November 16 memo.

Mr. Biden narrowly won Arizona, but two executives responsible for the accurate election night call lost their jobs because of it two months later. In an internal memo, Mr. Murdoch talked in mid-November about firing them.

Fox executives and anchors discussed how not to alienate the audience, many of whom believed Mr. Trump’s claims of fraud despite no evidence to back them up. A Fox host, Tucker Carlson, suggested a news reporter be fired for tweeting a fact check debunking the fraud claims.

Some of the exhibits were simply embarrassing, such as scornful behind-the-scenes opinions about Mr. Trump, whose supporters form the core of the network’s viewers. 

Text exchanges revealed as part of the lawsuit show Mr. Carlson declaring, “I hate him passionately,” and saying that “we are very, very close to being able to ignore Trump most nights.”