US State Department spokeswoman Heather Nauert said earlier the US would hold North Korea accountable for Warmbier's "unjust imprisonment" and called for the release of three other Americans detained in the country.
Senator John McCain said overnight that Americans who are "stupid" enough to still want to travel to North Korea should be required to sign a waiver absolving the United States government of any blame should they be harmed while there.
The U.S. government says North Korea is using such detainees as political pawns.
An Ohio coroner will not perform an autopsy on the USA student who died after being held prisoner in North Korea for 17 months and will perform an external examination of the body at the family's request.
On Monday, the 22-year-old Warmbier died in a Cincinnati hospital, days after his medical evacuation home, the victim of his treatment at the hands of North Korea.
Doctors at the Cincinnati Medical Center, where Mr Warmbier was treated following his return to the USA on 13 June, determined he suffered from "unresponsive wakefulness", also known as persistent vegetative state, due to "severe neurological injury".
Trump said Tuesday he had spoken with Warmbier's parents, telling reporters in the Oval Office that it was "incredible what they've gone through".
The death this week of an American university student held prisoner for 17 months by North Korea left OH municipal worker Jeffrey Fowle shaken. People can live in a state of unresponsive wakefulness for many years with the chances of recovery depending on the extent of the brain injury.
George Hunziker said his brother was young like Warmbier and did not realize the seriousness of his actions. "It puts us in a really precarious situation when Americans are detained there". "We are doing according to our national laws, and according to the worldwide standards", Han said, adding that he was not an expert on detention issues. Like student Otto Warmbier, he visited North Korea with a tour group and was taken into custody at the airport when trying to leave.
"I think we should strongly consider it", Corker said, per the AP. However, on 13 June Warmbier was sent back to his country in a state of coma on "humanitarian grounds". A naturalized US citizen who was born in South Korea, he is a businessman in his mid-60s who at one time lived in Fairfax, Virginia.
Young Pioneer Tours said on its Facebook page that the death of Warmbier shows that the risk American tourists face in visiting North Korea "has become too high".
While almost all Americans who have gone to North Korea have left without incident, some have been seized and given draconian sentences for seemingly minor offenses.
USA college student Otto Warmbier died Monday, days after his release from North Korea.
Hamilton County 's Dr. Lakshmi Sammarco's office released a statement saying Otto Warmbier's family objected to an autopsy so only an external exam of his body was done. It's impossible to know what the cause of death was, but specialists revealed that it had to do with a lack of oxygen reaching his brain.