In the latest volley in the battle over disinformation in the presidential election, Rupert Murdoch’s Fox Corporation has been sued by an obscure tech company that has accused his cable networks of defamation and contributing to the fervor that led to the siege of the Capitol.

The suit pits Smartmatic, which provided election technology in one county, against Donald J. Trump’s longtime favorite news outlet and three Fox anchors, Maria Bartiromo, Lou Dobbs and Jeanine Pirro, all ardent supporters of the former president. A trial could reveal how Mr. Trump’s media backers sought to cast doubt on an election that delivered a victory to Joseph R. Biden Jr. and a loss to an incumbent who refused to accept reality.

Filed in New York State Supreme Court, Smartmatic’s suit seeks at least $2.7 billion in damages. In addition to Mr. Murdoch’s Fox Corporation, Fox News and the three star anchors, it targets Rudolph W. Giuliani and Sidney Powell, lawyers who made the case for election fraud as frequent guests on Fox programs while representing President Trump.

In its 276-page complaint, Smartmatic, which has requested a jury trial, argues that Mr. Giuliani and Ms. Powell “created a story about Smartmatic” and that “Fox joined the conspiracy to defame and disparage Smartmatic and its election technology and software.”

“The story turned neighbor against neighbor,” the complaint continues. “The story led a mob to attack the U.S. Capitol.”

Smartmatic filed the suit three months after an election repeatedly described as rigged or stolen by Mr. Trump and his supporters. Fox and its upstart competitors Newsmax and OANN gave significant broadcast time to hosts and commentators who argued against the election’s integrity at a time of a rancorous political divide, when conspiratorial notions have moved into the mainstream.

Smartmatic’s suit follows two others filed last month by Dominion Voting Systems: one against Mr. Giuliani, the other against Ms. Powell. Dominion, a Smartmatic competitor, is another company that has figured prominently in baseless election-fraud theories.

Even after the storming of the Capitol on Jan. 6, a deadly riot led by Trump loyalists, the talk of fraud has not fully died down. In an appearance on Tuesday on Newsmax, Mike Lindell, the MyPillow founder who has been one of Mr. Trump’s devoted supporters, began an attack on Dominion. In a sign that the threat of defamation lawsuits has deterred media outlets that have broadcast conspiracy theories, the Newsmax anchor Bob Sellers cut off Mr. Lindell and read a statement: “The election results in every state were certified. Newsmax accepts the results as legal and final. The courts have also supported that view.”

In its complaint, Smartmatic said Fox programs became a venue for a number of falsehoods about the company in the weeks after the election, a time when powerful Republicans in Congress were sowing doubts about the vote’s outcome and Senator Mitch McConnell of Kentucky, then the majority leader, had yet to congratulate Joseph R. Biden Jr. on his victory.

The suit cites a false claim, made by Ms. Powell on a November episode of Mr. Dobbs’s show on Fox Business, that Hugo Chávez, the deceased president of Venezuela, had a hand in the creation of Smartmatic technology, designing it so that the votes it processed could be changed undetected. (Mr. Chávez, who died in 2013, did not have anything to do with Smartmatic.)

The lawsuit also cites exchanges on Fox programs that it says helped spread the claim that it was the owner of Dominion (it is not) and that it had provided its services to districts in contested states. (In fact, Smartmatic was used in the 2020 election only by Los Angeles County.) The lawsuit also says that Fox helped promote the false notion that the company had sent votes to other countries to be manipulated.

Smartmatic added in its complaint that Fox’s broadcasting of the false claims “jeopardized” its “multibillion-dollar pipeline of business”; damaged its election technology and software businesses; and made it difficult for the company to get new business in the United States, where it had made inroads after years of servicing elections in other nations.

A Fox spokeswoman disputed the claims in Smartmatic’s lawsuit, saying in a statement: “Fox News Media is committed to providing the full context of every story with in-depth reporting and clear opinion. We are proud of our 2020 election coverage and will vigorously defend this meritless lawsuit in court.”

Ms. Powell, who said she had not seen or received notice of the suit, said: “Your characterization of the claims shows that this is just another political maneuver motivated by the radical left that has no basis in fact or law.”

Ms. Bartiromo, Mr. Dobbs, Ms. Pirro and Mr. Giuliani did not immediately reply to requests for comment.

In its frontal attack on Mr. Murdoch’s company, Smartmatic argues that Fox cast it as a villain in a fictitious narrative meant to help win back viewers from Newsmax and OANN. Those two networks saw ratings surges in the weeks after the election, thanks to their embrace of the fiction that Mr. Biden was not the rightful victor. The Smartmatic suit also argues that Mr. Giuliani and Ms. Powell sought to enrich themselves and improve their standing with Mr. Trump’s supporters by making claims that were damaging to the company.

After Smartmatic sent a letter to Fox requesting a retraction for what it called “false and misleading statements” about the company and threatening legal action, each of the shows led by the three Fox anchors aired a segment in which an election expert, Eddie Perez, debunked a number of false claims about Smartmatic. The prerecorded segment, broadcast in December, showed Mr. Perez responding to questions from an off-camera voice. In an interview on Wednesday, Mr. Perez said that the finished product “almost looked like a deposition.”

Smartmatic’s complaint described not only the reputational and financial damage the company said it had suffered, but also the harm done to the United States by the claims promoted by Mr. Trump’s allies and the Murdoch-controlled networks he had long favored.

Fox Corporation, with about 9,000 employees, is run by Mr. Murdoch, 89, and his elder son, Lachlan, its chief executive. A penalty of $2.7 billion would be hefty. Fox Corporation made $3 billion in pretax profit on $12.3 billion in revenue from September 2019 to September of last year. The company is valued at about $17.8 billion.

Ms. Bartiromo, the host of shows on Fox Business and Fox News, conducted an interview with Mr. Trump on Nov. 29, his first lengthy TV interview after the election. Ms. Pirro, a onetime prosecutor whose “Justice with Judge Jeanine” is a staple of Fox News’s Saturday night lineup, has been friends with Mr. Trump for decades.

Don Herzog, who teaches First Amendment and defamation law at the University of Michigan, said that the suit’s main argument made sense. “You can’t just make false stuff up about people,” he said. He expressed doubt about the suit’s linking the false statements on Fox to the Capitol attack, however, saying the events of Jan. 6 had no bearing on whether the defendants had harmed Smartmatic.

The suit’s success would depend on a variety of factors, Mr. Herzog added, including whether Smartmatic can persuade a jury that the company did not have the standing of a public figure before Mr. Giuliani and Ms. Powell made it better known.

If the court determines that Smartmatic was a public figure, the burden of proof for its claims will be higher. The company will have to show that the defendants knew that their statements were false or that they had serious doubts about them. In its complaint, Smartmatic argues that Mr. Giuliani, Ms. Powell and the three Fox anchors acted with “actual malice” and “recklessly disregarded” the veracity of their statements.

While it may be difficult to persuade jurors that Fox is responsible for what guests say on its programs, Timothy Zick, a William & Mary Law School professor who specializes in First Amendment law, said the company could be held responsible for the content of its broadcasts.

“If they knew that the segment was going to include these false statements, then I don’t think that relieves them of liability,” he said.

At times, the language of the Fox hosts echoed that of Mr. Trump’s lawyers. The lawsuit cites Ms. Powell referring to the supposed vote-fraud conspiracy as a “cyber Pearl Harbor,” a phrase repeated by Mr. Dobbs on his show and on Twitter.

When Smartmatic started in April 2000, it offered its services to banks. The shift to election security came after Antonio Mugica, a company founder and its chief executive, was in Palm Beach County during the contested 2000 election. “We were in the first row watching that circus,” he said. “And it really caused an impact on all of us.”

The company had success providing its electronic voting machines, online voting platforms and software products for elections around the world. It was also used in the 2016 Republican presidential caucus in Utah. In 2018, Los Angeles County chose Smartmatic to develop a new election system, and its technology was used there in the March presidential primary and again in the general election.

After Election Day, the company’s name, along with that of Dominion, became integral to the baseless theories promoted by right-wing media outlets. Smartmatic employees and their family members received threats, including death threats, some of which were noted in the complaint.

“I had one in which I was told they were going to actually come kidnap me in London, where I was at the time,” Mr. Mugica said. “They were sending three people. ‘Plane is landing tomorrow.’”

Edmund Lee contributed reporting. Kitty Bennett contributed research.