USA and Chinese diplomats and defense chiefs are meeting later Wednesday in Washington for security talks.
The government of China, North Korea's main ally, said Warmbier's death was a tragedy.
Trump added: "At least I know China tried".
Otto Warmbier's death after returning from North Korean imprisonment is stoking outrage in Washington and threatening to overshadow high-level U.S.
Chris Coons wonders why anyone still travels to North Korea, and says the death of American student Otto Warmbier after a year-long imprisonment in the communist dictatorship is "tantamount to murder".
Watch crowd shout 'Trump! Trump! Trump!' at victory speech
He urges Democrats to look into races previously not on the radar or thought to be competitive and stop the second guessing. Barbara Boxer (D-California), said Ossoff's loss was "tough", but Democrats, "can and will do better in 2018".
The college student died shortly after his return to OH after being held for more than 17 months. Warmbier was arrested while visiting as a tourist and accused of trying to steal an item bearing a propaganda slogan, according to North Korean media.
Moon took the opportunity to urge Pyongyang to return other South Korean and U.S. citizens held there, vowing to make all-out efforts for their release.
Earlier the coroner's office said it had received Warmbier's body for an autopsy examination and was expecting to release preliminary findings later on Tuesday or on Wednesday.
Tillerson reiterated the Trump administration's argument that China has the "diplomatic responsibility to exert pressure greater to prevent further escalation in the region". "U.S.A.", he had tweeted in April.
For months, Trump, Vice President Mike Pence and top aides have staked any progress dealing with North Korea's burgeoning nuclear programme on China's involvement.
"I think there have been some positive steps that they've taken, both at the United Nations and economically, to help strengthen the case against North Korea".
Warmbier said it was his understanding that, at Trump's direction, State Department officials "aggressively pursued" a resolution.
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