With a series of billion-dollar lawsuits, including a $1.6 billion case against Fox News headed to trial this month, Dominion Voting Systems sent a stark warning to anyone spreading falsehoods that the company’s technology contributed to fraud in the 2020 election: Be careful with your words, or you might pay the price.

Not everyone is heeding the warning.

“Dominion, why don’t you show us what’s inside your machines?” Mike Lindell, the MyPillow executive and prominent election denier, shouted during a livestream last month. He added that the company, which has filed a $1.3 billion defamation lawsuit against him, was engaged in “the biggest cover-up for the biggest crime in United States history — probably in world history.”

Claims that election software companies like Dominion helped orchestrate widespread fraud in the 2020 election have been widely debunked in the years since former President Donald J. Trump and his allies first pushed the theories. But far-right Americans on social media and influencers in the news media have continued in recent weeks and months to make unfounded assertions about the company and its electronic voting machines, pressuring government officials to scrap contracts with Dominion, sometimes successfully.

The enduring attacks illustrate how Mr. Trump’s voter fraud claims have taken root in the shared imagination of his supporters. And they reflect the daunting challenge that Dominion, and any other group that draws the attention of conspiracy theorists, faces in putting false claims to rest.

The attacks about Dominion have not reached the fevered pitch of late 2020, when the company was cast as a central villain in an elaborate and fictitious voter fraud story. In that tale, the company swapped votes between candidates, injected fake ballots or allowed glaring security vulnerabilities to remain on voting machines.

Dominion says all those claims have been made without proof to support them.

“Nearly two years after the 2020 election, no credible evidence has ever been presented to any court or authority that voting machines did anything other than count votes accurately and reliably in all states,” Dominion said in an emailed statement.

On Friday, the judge in Delaware overseeing the Fox defamation case ruled that it was “CRYSTAL clear” that Fox News and Fox Business had made false claims about the company — a major setback for the network.

Many prominent influencers have avoided mentioning the company since Dominion started suing prominent conspiracy theorists in 2021. Fox News fired Lou Dobbs that year — only days after it was sued by Smartmatic, another election software company — saying the network was focusing on “new formats.” Mr. Dobbs is also a defendant in Dominion’s case against Fox, which is scheduled to go to trial on April 17.

Yet there have been nearly nine million mentions of Dominion across social media websites, broadcasts and traditional media since Dominion filed its first lawsuit in January 2021, including nearly a million that have mentioned “fraud” or related conspiracy theories, according to Zignal Labs, a media monitoring company. Some of the most widely shared posts came from Representative Marjorie Taylor Greene, Republican of Georgia, who tweeted last month that the lawsuits were politically motivated, and Kari Lake, the former Republican candidate for governor of Arizona who has advanced voter fraud theories about election machines since her defeat last year.

Mr. Lindell remains one of the loudest voices pushing unproven claims against Dominion and electronic voting machines, posting hundreds of videos to Frank Speech, his news site, attacking the company with tales of voter fraud.

Last month, Mr. Lindell celebrated on his livestream after Shasta County, a conservative stronghold in Northern California, voted to use paper ballots after ending its contract with Dominion. A county supervisor had flown to meet privately with Mr. Lindell before the vote, discussing how to run elections without voting machines, according to Mr. Lindell. The supervisor ultimately voted to switch to paper ballots.

In an interview this week with The New York Times, Mr. Lindell claimed to have spent millions on campaigns to end election fraud, focusing on abolishing electronic voting systems and replacing them with paper ballots and hand counting.

“I will never back down, ever, ever, ever,” he said in the interview. He added that Dominion’s lawsuit against him, which is continuing after the United States Supreme Court declined to consider his appeal, was “frivolous” and that the company was “guilty.”

“They can’t deny it, nobody can deny it,” Mr. Lindell said.

Joe Oltmann, the host of “Conservative Daily Podcast” and a promoter of voter fraud conspiracy theories, hosted an episode in late March titled “Dominion Is FINISHED,” in which he claimed that there was a “device that’s used in Dominion machines to actually transfer ballots,” offering only speculative support.

“This changes everything,” Mr. Oltmann said.

Dominion sent Mr. Oltmann a letter in 2020 demanding that he preserve documents related to his claims about the company, which is often the first step in a defamation lawsuit.

In a livestream last month on Rumble, the streaming platform popular among right-wing influencers, Tina Peters, a former county clerk in Colorado who was indicted on 10 charges related to allegations that she tampered with Dominion’s election equipment, devoted more than an hour to various election fraud claims, many of them featuring Dominion. The discussion included a suggestion that because boxes belonging to Dominion were stamped with “Made in China,” the election system was vulnerable to manipulation by the Chinese Communist Party.

Mr. Oltmann and Ms. Peters did not respond to requests for comment.

The Fox lawsuit has also added fuel to the conspiracy theory fire.

Far-right news sites have largely ignored the finding that Fox News hosts disparaged voter fraud claims privately, even as they gave them significant airtime. Instead, the Gateway Pundit, a far-right site known for pushing voter fraud theories, focused on separate documents showing that Dominion executives “knew its voting systems had major security issues,” the site wrote.

The documents showed the frenzied private messages between Dominion employees as they were troubleshooting problems, with one employee remarking, “our products suck.” In an email, a Dominion spokeswoman noted the remark was about a splash screen that was hiding an error message.

In February, Mr. Trump shared the Gateway Pundit story on Truth Social, his right-wing social network, stoking a fresh wave of attacks against the company.

“We will not be silent,” said one far-right influencer whose messages are sometimes shared by Mr. Trump on Truth Social. “Dominion is the enemy!”