The Warmbiers say their son was tortured after being convicted of trying to steal a propaganda poster and imprisoned for months.
He suffered severe brain damage, but doctors were unable to determine was led to it. The 22-year-old died days after being returned to the U.S. in a vegetative state in 2017.
"The Warmbiers are committed to holding North Korea accountable for the death of their son Otto, and will work tirelessly to seize North Korean assets wherever they may be found," Ben Hatch, an attorney for the family, said in an emailed statement.
North Korea has rejected accusations by relatives that it tortured Warmbier and said he was provided "medical treatments and care with all sincerity."
North Korea did not respond to the wrongful death lawsuit that accused it of detaining Warmbier at the Pyongyang airport "in an attempt to extract various concessions from the United States government."
U.S. District Judge Beryl Howell ruled last year that North Korea "more likely than not barbarically tortured Otto to extract a false confession" and used his lengthy prison sentence as leverage to further its foreign policy objectives.
She ordered North Korea to pay $501 million for its "barbaric mistreatment" of Warmbier, saying the student's family "experienced North Korea's brutality first-hand."
In the latest court filings, Warmbier's parents claim a right to the North Korean cargo ship, which the U.S. seized in May because it was carrying coal in violation of U.N. sanctions.
The vessel, North Korea's second-largest cargo ship, was first detained in April 2018 by Indonesia while transporting a large amount of coal. The U.S. later announced it had seized the 17,061-ton carrier in a first-of-its kind enforcement that came amid a tense moment in relations with North Korea.