He called North Korea a "brutal regime".
Prominent Republican senator John McCain was highly critical of North Korea's actions in imprisoning the OH student.
Warmbier's family said they believed the student had found peace after being flown home.
Moon's interview came ahead of his scheduled visit to the United States next week for summit meetings with his US counterpart Donald Trump.
"I can not understand what the Warmbier family is feeling right now". Doctors had described Warmbier's condition as a state of "unresponsive wakefulness" and said he suffered a "severe neurological injury" of unknown cause. He had suffered significant brain damage during his imprisonment.
Warmbier's parents announced their son's death in a statement on Monday evening (19 June), saying that he had been subjected to "awful torturous mistreatment" adding they were glad he "completed his journey home". A former University of Virginia student, he was serving a 15-year sentence in North Korea for allegedly attempting to steal a banner containing a political phrase that was hanging from a wall in his Pyongyang hotel.
Otto Warmbier arrives at court for his trial in Pyongyang on March 16, 2015. It was to be a brief stay followed by a visit to Beijing.
The circumstances of Mr Warmbier's detention in North Korea remain a mystery, but relatives argue his condition suggests that he had been physically abused by his captors.
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However, the government had not acted on the recommendations of the report, with the minister responsible Gavin Barwell saying he was reviewing it.
He admitted to the crime and begged for forgiveness.
The company, Young Pioneer Tours, said Tuesday that it would no longer take Americans to North Korea because the "assessment of risk" was too high. "The way his detention was handled was appalling, and a tragedy like this must never be repeated", it said.
Warmbier, "Please save my life". The company also noted that no previous detainment of a tourist in North Korea "has ended with such tragic finality" and emphasized this must not be repeated.
Moon's remarks on CBS's "This Morning" programme came the day after the death of Otto Warmbier, the 22-year-old student who had been held prisoner in North Korea for 17 months.
FILE - In this February 29, 2016, file photo, American student Otto Warmbier speaks as he is presented to reporters in Pyongyang, North Korea.
SEOUL, South Korea (AP) - North Korea's missile and nuclear tests, its carefully scripted propaganda bluster, even its military threats: Far from the scattershot workings of a madman, most of this fits the playbook of a small, proud country well used to stoking tensions to get concessions it would otherwise not receive from surrounding big powers.
In response, President Donald Trump issued a terse statement condemning North Korea, which is still holding three Americans hostage.
But American tourists make up only a small fraction of visitors to North Korea, whose tourism industry is dominated by visitors from China, its main economic partner.
Three US citizens and a Canadian pastor are still being detained in North Korea.
The statement said the family Warmbier, he passed away at 14.20 (21.20 Kiev) medical center in Cincinnati.
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