Otto Warmbier, 22, died in June a few days after he was sent home in a mysterious coma following more than a year in prison in North Korea.
He had been convicted of offenses against the state for trying to steal a propaganda poster from a Pyongyang hotel and sentenced to 15 years' hard labour.
No US official had previously publicly accused North Korea of torture in the case.
Trump's comment today on Twitter followed the airing of a Fox News interview with Warmbier's parents.