Fred and Cindy Warmbier made the claim on Friday as they rebuked Donald Trump.
The US President told a press conference he had taken the authoritarian leader "at his word" when he said he was not aware of alleged mistreatment against Otto Warmbier.
Mr Trump spoke after a meeting he held with Mr Kim in Vietnam this week. The two leaders failed to reach an agreement about denuclearisation in North Korea.
The Warmbiers said "Kim and his evil regime are responsible for the death of our son Otto" and for "unimaginable cruelty and inhumanity".
"No excuses or lavish praise can change that", they added.
They claimed they had kept silent during the summit in Hanoi, but "now we must speak out".
Otto Warmbier was sentenced to 15 years in prison and hard labour after he was accused of trying to steal a propaganda poster in a hotel for his church, during a visit with a China-based holiday tour company.
The Ohio man, who attended the University of Virginia, died in June 2017 - days after North Korea released him on humanitarian grounds.
He was returned home in a vegetative state. North Korea has always denied cruelty or torture.
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