Republicans have put pressure on the White House to act over the death of US uni student Otto Warmbier, saying North Korea murdered him.

Senators John McCain and Marco Rubio did not mince their words as they expressed outrage over the death of the 22-year-old, who was released back to the US last week in a coma and later died.

"Otto Warmbier should never have been in jail for tearing down a stupid banner. And he most certainly should not have been murdered for it," Senator Rubio said.

Otto Warmbier should never have been in jail for tearing down a stupid banner. And he most certainly should not have been murdered for it.

— Marco Rubio (@marcorubio) June 19, 2017

Senator McCain also slammed North Korea saying, "Let us state the facts plainly: Otto Warmbier, an American citizen, was murdered by the Kim Jong-un regime."

US Secretary of State Rex Tillerson has flagged a potential travel ban to North Korea.

US President Donald Trump called Warmbier's detainment and death a "total disgrace."

The president on Tuesday said that if Warmbier had been returned home to the US earlier, "I think the result would have been a lot different."

Trump spoke briefly about Warmbier during an Oval Office meeting with the president of Ukraine.

He said he spoke with Warmbier's parents, adding it's "incredible what they've gone through" and that the student "should have been brought home a long time ago."

It came as the travel agency that organised Warmbier's North Korea says it will no longer take US citizens to the country.

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."

Warmbier died in Ohio on Monday, days after being released by North Korea while in a coma.

The tour operator said that it was denied any opportunity to meet with Warmbier after his detention, and that the way it was handled was "appalling."

The travel agency specialises in North Korea tours and is based in the central Chinese city of Xi'an.

Other well-known North Korea tour operators, including Koryo Tours, founded by British expatriates in Beijing, and Uri Tours, with offices in New Jersey and Shanghai, said this week that they were 'reviewing' their policies for American citizens.

The coroner's office in Cincinnati is investigating Warmbier's death.

A spokesman for the Hamilton County coroner says Dr Lakshmi Sammaraco's office has accepted the case.

Justin Weber said that a press conference is expected later to provide details.

Warmbier's parents did not cite a specific cause of death, but cited "awful, torturous mistreatment" by North Korea.

Doctors had described Warmbier's condition as a state of "unresponsive wakefulness" and said he suffered a "severe neurological injury" of unknown cause.

It comes as South Korean President Moon Jae-in says North Korea should swiftly return South Koreans and Americans detained in the reclusive nation and that Pyongyang has "a heavy responsibility" in the death of Warmbier.

President Moon, who is scheduled to visit Washington next week, also said in an interview with CBS on Tuesday he hoped to draw North Korea into negotiations on its nuclear program by the end of the year.

He said that while "we cannot know for sure that North Korea killed Mr Warmbier ... I believe it is quite clear that they have a heavy responsibility in the process that led to Mr Warmbier's death. "I believe we must now have the perception that North Korea is an irrational regime."

South Korea's Blue House on Tuesday cited President Moon separately as saying: "It is very deplorable that North Korea does not respect human rights."

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.

North Korea said last month that it was its sovereign right to "ruthlessly punish" US citizens it had detained for crimes against the state.