WASHINGTON—One of the largest voting-machine companies in the U.S. on Tuesday sued two conservative media networks and a businessman it said had defamed it by spreading accusations that it rigged the 2020 election for President Biden.

Dominion Voting Systems filed suits against Newsmax Media Inc. and Herring Networks Inc.’s One America News Network. Dominion also sued Patrick Byrne, the former chief executive of Overstock.com Inc., an online seller of furniture and other goods.

Dominion accused the two networks of defaming the company and its products by airing false reports that its machines switched votes from President Donald Trump to Mr. Biden. The company also said Mr. Byrne repeatedly and falsely alleged that Dominion rigged vote tallies to steal the 2020 presidential election for Mr. Biden. In each of the three lawsuits, Dominion is seeking more than $1.6 billion in damages, citing lost profit and other costs.

Former Overstock Chief Executive Patrick Byrne speaking to President Trump supporters at a rally in January.

Photo: Bryan Smith/Zuma Press

“Newsmax helped create and cultivate an alternate reality where up is down, pigs have wings, and Dominion engaged in a colossal fraud to steal the presidency from Donald Trump by rigging the vote,” the suit against Newsmax says.

Dominion sued Newsmax in state court in Delaware. The lawsuit against One America News Network, which also names executives Charles Herring and Robert Herring Sr. and reporters Chanel Rion and Christina Bobb as defendants, and the suit against Mr. Byrne were filed in federal court in the District of Columbia.

Newsmax said that it had not reviewed the suit but that in its coverage of the 2020 election it reported on allegations made by public figures including Mr. Trump, his advisers, and members of Congress.

“Dominion’s action today is a clear attempt to squelch such reporting and undermine a free press,” the network said.

One America News Network previously said in a disclaimer that it doesn’t endorse any opinions about Dominion. Representatives for One America News Network didn’t immediately respond to a request for comment.

Mr. Byrne previously has said that he didn’t vote for Mr. Trump, but that he believes the 2020 election was rigged. Mr. Byrne didn’t immediately respond to a request for comment.

Federal and state officials have said there is no evidence that any voting system deleted or changed votes in the November election. Election officials have recounted and audited millions of paper ballots in multiple states, which have affirmed the outcomes tabulated by Dominion’s machines.

The new lawsuits are the latest in a series of defamation lawsuits by Dominion, which has accused media outlets and prominent supporters of Mr. Trump of spreading falsehoods that Dominion rigged votes cast in the 2020 election.

As a result of those falsehoods, Dominion said in court filings it has lost out on contracts valued at a combined $90 million, and that its employees have faced harassment and death threats.

Dominion has already filed four other defamation lawsuits related to the 2020 election, seeking billions of dollars in damages. The suits have been against Fox News, Rudy Giuliani, MyPillow Inc. chief executive Mike Lindell and his company, and pro-Trump attorney Sidney Powell.

Fox News has moved to dismiss the lawsuit, saying its coverage of claims about election fraud was newsworthy and protected by the First Amendment. The others have sought to dismiss the suits against them. Mr. Lindell also has countersued.

Write to Alexa Corse at alexa.corse@wsj.com