Lawyers for the families of two Sandy Hook shooting victims are accusing the conspiracy theorist Alex Jones and his Infowars media business of intentionally destroying evidence relevant to the defamation cases against him, according to a motion filed on Friday in a Texas court.

Mr. Jones is being sued by the families of nine Sandy Hook victims for spreading false claims that the 2012 shooting at the elementary school in Newtown, Conn., that killed 20 first graders and six adults was a government-backed hoax, and that the families of the dead were actors.

Mr. Jones said on his broadcast last week that he had told his staff to delete material after CNN cited Infowars content that violated Twitter’s policies, according to the motion filed on Friday.