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Otto Warmbier (22), who was arrested in North Korea while visiting as a tourist, had been described by doctors who examined him last week as having suffered extensive brain damage that left him in a state of "unresponsive wakefulness."
"Unfortunately, the awful torturous mistreatment our son received at the hands of the North Koreans ensured that no other outcome was possible beyond the sad one we experienced today," the family said in a statement following Warmbier's death at in Cincinnati at 2.20pm on Monday (local time).
There was no immediate word from Warmbier's family on the cause of his death.
They have said that the student lapsed into a coma in March 2016, shortly after he was sentenced to 15 years of hard labour in North Korea. He was arrested, according to North Korean media, for trying to steal an item bearing a propaganda slogan.
Physicians said last Thursday that Warmbier had shown no sign of understanding language or of awareness of his surroundings, and had made no "purposeful movements or behaviours" though he was breathing on his own.
The circumstances of his detention in North Korea and what medical treatment he may have received there remained a mystery, but relatives have said his condition suggested that he had been physically abused by his captors.
North Korea released Warmbier last week, saying he was being freed "on humanitarian grounds." The North Korean mission to the United Nations was not immediately available for comment.
The University of Virginia student's father, Fred Warmbier, said last week that his son had been "brutalised and terrorised by the Pyongyang government and that the family disbelieved North Korea's story that his son had fallen into a coma after contracting botulism and being given a sleeping pill.
Doctors who examined Otto Warmbier after his release said there was no sign of botulism in his system.
Warmbier was freed after the US State Department's special envoy on North Korea, Joseph Yun, traveled to Pyongyang and demanded the student's release on humanitarian grounds, capping a flurry of secret diplomatic contacts, a US official said last week.
Tensions between the United States and North Korea have been heightened by dozens of North Korean missile launches and two nuclear bomb tests since the beginning of last year. Pyongyang has also vowed to develop a nuclear-tipped intercontinental ballistic missile capable of hitting the US mainland.
US President Donald Trump offered condolences to the Warmbier family and denounced North Korea as a “brutal regime” with no respect for "basic human decency" and said Warmbier faced tough conditions.
Secretary of State Rex Tillerson said the United States holds North Korea accountable for Warmbier's "unjust imprisonment" and demanded the release of three other US citizens still held by Pyongyang - Korean-Americans Tony Kim, Kim Dong Chul and Kim Hak Song.
Jonathan Bae, whose father, Korean-American missionary Kenneth Bae spent two years in North Korean captivity before his release in 2014, expressed sadness at Warmbier's death.
"My heart goes out to the family. I will pray for them and hope they find peace."
Young Pioneer Tours, the group with which Warmbier traveled to North Korea, will no longer be organising tours for US citizens to the isolated country, Troy Collings, a company director at the group, said in a statement.