Dominion Voting Systems sued Mike Lindell, chief executive of Minnesota-based MyPillow Inc., and his company in the U.S. District Court for the District of Columbia, seeking more than $1.3 billion in damages.

In its complaint, the company cites a number of statements made by Mr. Lindell, including in media appearances, social-media posts, and a two-hour film claiming to prove widespread election fraud. Mr. Lindell said he helped produce the film, which he released online in early February.

The complaint alleges that Mr. Lindell made false claims about the integrity of Dominion’s voting machines and that he knew no credible evidence supported his claims that the company had stolen the election from Mr. Trump—what Dominion has called the “Big Lie.”

“He is well aware of the independent audits and paper ballot recounts conclusively disproving the Big Lie,” the complaint states. “But Lindell…sells the lie to this day because the lie sells pillows.”