Fred and Cindy Warmbier, of suburban Cincinnati, sued in April in federal court in Washington. North Korean authorities arrested their son in January 2016 for stealing a propaganda poster. He was sentenced to 15 years in prison.
The 22-year-old died in 2017, days after he was repatriated to the U.S. with severe brain damage.
The Cincinnati Enquirer reports a motion filed in October in the lawsuit seeks $1.05 billion in punitive damages and about $46 million for the family's suffering.
North Korea has repeatedly denied the accusations that it tortured Warmbier.