Doctors in Cincinnati said they found no active sign of botulism - a toxin that causes nerve damage - or evidence of beatings.
On Twitter, Republican Senator Marco Rubio wrote that Warmbier "should never have been in jail for tearing down a stupid banner".
It is unclear why the family objected to an autopsy which could answer what happened to Warmbier in the secretive nation. China is the North's only major trading partner, so a threat to limit commerce if North Korea doesn't change would be the natural way to try to push Kim around.
The president says if Otto Warmbier had been returned home to the US earlier, "I think the result would have been a lot different".
Mr Trump spoke briefly about Warmbier during an Oval Office meeting with the president of Ukraine.
President Donald Trump also commented on the student's treatment Tuesday, saying he thought Otto Warmbier "should have been brought home a long time ago".
"I believe we must now have the perception that North Korea is an irrational regime", said Moon, who was elected in May.
In addition, between 800 and 1,250 Americans visited North Korea annually in past years, according to tour companies working in the reclusive country.
Warmbier was released from a North Korean prison last week and was sent back home in a coma, a condition he had been in for more than a year in a coma.
"It's unlikely that Washington and Seoul will let Warmbier's death entirely derail their efforts at talks because North Korea's nuclear weapons program is such a serious and immediate threat", said Koh Yu-hwan, a North Korea expert at Seoul's Dongguk University. Young Pioneer Tours said Tuesday on Facebook that his death shows that the risk American tourists face in visiting North Korea "has become too high".
Warmbier grew up in the Cincinnati suburb of Wyoming.
Spicer: Warmbier's Death a 'Shame,' China Needed to Help More
It remains unclear what caused the University of Virginia student's severe health problems when he was in North Korea . Why? To make a political point, to show the USA that this is what you get if you mess with North Korea .
A spokesman for the Hamilton County coroner says Dr Lakshmi Sammaraco's office has accepted the case. Justin Weber told The Associated Press on Tuesday morning that a press conference is expected later to provide details.
"The bad torturous mistreatment our son received at the hands of the North Koreans ensured that no other outcome was possible", the family said Monday announcing Warmbier's death.
Warmbier had not spoken or moved in any purposeful way since his return, a condition his doctors called "unresponsive wakefulness" also known as persistent vegetative state.
President Trump called the death of Otto Warmbier, an American recently released after being held by North Korean authorities, a "disgrace", on June 20 at the White House.
"While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out", he tweeted.
They said Warmbier's severe brain injury was most likely - given his young age - to have been caused by cardiopulmonary arrest cutting the blood supply to the brain.
Even as Warmbier's family prepared to mourn him at a public funeral service Thursday in OH, the circumstances behind his death remained unclear.
"The United States once again condemns the brutality of the North Korean regime as we mourn its latest victim".
Pyongyang returned Warmbier to the US on June 13 after reportedly being in a coma for a year.
American special envoys reportedly told Warmbier's family that North Korean officials said he had contracted botulism soon after his trial, and had taken a sleeping pill and slipped into a coma.
While that might not be palatable to many following the tragic death of Warmbier, especially following Pyongyang's risible missile tests and threats over the last several months, engaging with the North Koreans can potentially help reduce tensions in the future.
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