President Donald Trump said he was running out of patience with the North Korean regime. Friday a spokesman claimed his death was a mystery.
Warmbier, 22, was arrested while visiting the reclusive country as a tourist.
The North Koreans said that constituted a "hostile act" - and sentenced him to 15 years of hard labor.
He died on Monday at a Cincinnati hospital and was buried on Thursday.
North Korea repeated accusations that Warmbier had been instructed to steal the poster by the secretive Z-Society associated with the University of Virginia, where he went to school. Hunziker was detained in North Korea for months in 1996 for illegally crossing the border and committed suicide less than a month after he returned to the United States later that year.
"Unfortunately, the very bad, 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", Warmbier's parents said in announcing their son's death Monday. It rebuffed "groundless public opinion now circulating in the U.S. that he died of torture and beating during his reform through labor".
North Korea accepted repeated requests from the present USA administration, the spokesman said, and repatriated the student on humanitarian grounds "in consideration of his bad health".
The agency said: "Our related institutions are treating criminals who committed crimes against (our) republic strictly based on domestic law and global standards, and Warmbier was no different", the KCNA said.
Those who have "absolutely no idea" about "how well" Pyongyang treated Warmbier "under humanitarian conditions dare to utter "mistreatment" and "torture"," the statement from the official read.
Warmbier was sent back to the U.S.in a state of unresponsive wakefulness, according to doctors at the University of Cincinnati Medical Center.
Doctors said the released detainee suffered a severe brain damage.
US officials have not been able to provide a cause of death for Warmbier, in part because his family objected to an autopsy being performed.
Dr. Calvin Sun, founder of travel guide company Monsoon Diaries, went to North Korea with Young Pioneer Tours in 2011.
Now they have accused America of carrying out a "smear campaign" in the wake of Mr Warmbier's death.
Mattis said that they also discussed the importance of freedom of navigation, peaceful resolution of maritime disputes and ways to decrease tension in the South China Sea. "Otto's fate deepens my administration's determination to prevent such tragedies from befalling innocent people at the hands of regimes that do not respect the rule of law or basic human decency". In his memoir, Not Forgotten: The True Story of My Imprisonment in North Korea, he said how one interrogator kept telling him: "No one remembers you".
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