But American tourists make up only a small fraction of visitors to North Korea, whose tourism industry is dominated by visitors from China, its main economic partner.
North Korea has detained two Korean-American academics and a missionary, a Canadian pastor and three South Korean nationals who were doing missionary work there.
The student's death elicited strong repudiations of the regime from the highest levels of the American government. However, similar warnings on the limits of American diplomatic efforts toward North Korea, a country with which the United States does not have formal diplomatic relations, have not seemed to deter travelers to date.
Warmbier, an OH native and student at the University of Virginia, was arrested in North Korea in January 2016 while visiting as a tourist.
Otto Warmbier died at the age of 22 in a Cincinnati hospital on Monday, just days after the North Korean government sent him home in a coma and suffering from extensive brain damage, according to the USA doctors who treated him.
Another cautioned against reading too much into the message, arguing that there was no meeting earlier in the day that could have spurred the comment or that that tweet foretold some sort of unilateral action against North Korea. John McCain, R-Ariz., proposed that prospective American travelers complete a form declaring they won't hold the US government responsible for what happens.
Details on Warmbier's funeral service were released Tuesday by Spring Grove Cemetery and Arboretum.
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.
He was salutatorian of his 2013 Wyoming High School class before attending the University of Virginia.
The U.S. government says North Korea uses the detainees for political reasons.
Speaking from the White House Trump said: "He spent a year and half in North Korea, a lot of bad things happened, but at least we got him home to be with his parents".
Working with China on North Korea 'has not worked out'
President Donald Trump said on Tuesday he had spoken with Warmbier's family and praised them as "incredible". Warmbier's family said they believed the student had found peace after being flown home.
The coroner's office in Cincinnati is investigating the death of an American college student who died less than a week after his return from North Korea, where he was detained for almost a year and a half.
The Trump administration is considering banning travel by US citizens to North Korea, officials said Tuesday, as outrage grew over the death of American student Otto Warmbier and President Donald Trump declared it a "total disgrace". "And the two of us also share the common goals of resolving the North Korean nuclear issue, establishing a peace regime on the Korean Peninsula, and building peace and security in Northeast Asia", Moon said.
On June 12, North Korea released Otto Warmbier, an American who had been held since January of 2016 after allegedly stealing a propaganda poster.
The younger Warmbier grew up in the Cincinnati suburb of Wyoming.
He had had planned to study in China in his third year of college and heard about Chinese travel companies offering trips to North Korea.
Relatives say Otto Warmbier died Monday.
Young Pioneer Tours, which was founded by British expatriate Gareth Johnson, said that it was denied any opportunity to meet with Warmbier after his detention, and that the way it was handled was "appalling". He was sentenced to 15 years' hard labour in a gulag for "hostile acts against the DPRK".
His family said they were told he had been a coma since soon after his March 2016 sentencing.
This is why, for years, the State Department has advised American citizens against travelling to North Korea.
"We are discussing this matter frankly with our Korean travel partners, and the foreign organizations active in Pyongyang that we liaise with", Beijing-based Koryo Tours said in a statement.
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