“You’re trying to set me up with child porn,” Mr. Jones said. “One million dollars to put your head on a pike. ”

Norman Pattis, a lawyer for Mr. Jones, said that the allegation had already been investigated by the F.B.I. and that Mr. Jones had been cleared of any wrongdoing.

“For two weeks the F.B.I. conducted an inquiry and I learned on Wednesday of this week that that inquiry concluded that no one here has any guilty knowledge of those emails, indeed there is no reason to suspect anybody even knew they were here,” Mr. Pattis said on an Infowars broadcast on Saturday.

“The attempt to use this as a litigation club is the worst form of special pleading and the plaintiffs’ lawyers know it,” Mr. Pattis added.

Calls to the F.B.I. office in New Haven on Monday were not immediately returned.

“It is worth noting that if the Jones defendants had engaged in even minimal due diligence and actually reviewed the materials before production, they would have found the images themselves,” the lawyers for the families, who are with the law firm Koskoff Koskoff & Bieder, wrote in their filing.