Dominion Voting Systems sued Mike Lindell, the chief executive of MyPillow, on Monday, alleging that he defamed Dominion with baseless claims of election fraud involving its voting machines; it is seeking more than $1.3 billion in damages.

The complaint, filed in the United States District Court for the District of Columbia, alleges that Mr. Lindell “exploited” false claims about election fraud to support sales of his own business. Representatives for MyPillow could not immediately be reached to comment on the suit.

“Lindell — a talented salesman and former professional card counter — sells the lie to this day because the lie sells pillows,” the suit states, arguing that the company’s “defamatory marketing campaign” — with promo codes like “FightforTrump” and “QAnon” — increased MyPillow sales by 30 percent to 40 percent.

The company says it wrote to Mr. Lindell “multiple times,” putting him on “formal written notice of the facts” and informing him of “death threats” its employees have received.

“Instead of retracting his lies, Lindell — a multimillionaire with a nearly unlimited ability to broadcast his preferred messages on conservative media — whined that he was being ‘censored’ and ‘attacked’ and produced a ‘docu-movie’ featuring shady characters and fake documents sourced from dark corners of the internet,” the suit states.

Several retailers, including Bed Bath & Beyond and Kohl’s have stopped selling the company’s products in recent weeks. Twitter has permanently suspended his account.

Defamation suits against individuals and networks who shared former President Donald J. Trump’s election conspiracies have become a new front in the war against misinformation.

Dominion also filed defamation suits last month against two of the former president’s lawyers, Rudolph W. Giuliani and Sidney Powell. Another voter technology firm, Smartmatic, filed its defamation suit against Rupert Murdoch’s Fox empire in early February, saying its anchors Lou Dobbs, Maria Bartiromo and Jeanine Pirro harmed its business and reputation. Fox has filed a motion to dismiss that suit.