WASHINGTON (AP) -- 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.”

Secretary of State Rex Tillerson, who has the authority to cut off travel to North Korea with the stroke of the pen, has been weighing such a move since late April, when American teacher Tony Kim was detained in Pyongyang, a senior State Department official said. No ban is imminent, but deliberations gained new urgency after Warmbier’s death, said the official, who requested anonymity to discuss internal diplomatic discussions.

From Capitol Hill to the White House, pressure mounted for a tough US response, even as US diplomats sought to protect other Americans from facing a similar fate. Three other US citizens, including Kim, are still being held in North Korea.

“It’s a total disgrace what happened to Otto. That should never ever be allowed to happen,” Trump said in the Oval Office.

Suggesting former President Barack Obama bears some blame, Trump said “the result would have been a lot different” had Warmbier been brought home sooner. Obama’s office had no reaction, but his former aides have said he worked tirelessly to try to get Warmbier and other Americans released from North Korea.

Warmbier, 22, died Monday in his home state of Ohio, his family said, just days after being released in a coma by North Korea. The former University of Virginia student had been visiting North Korea on a tour group when he was detained, sentenced to 15 years of hard labor for subversion, and held for more than 17 months. The circumstances of his coma and death remain unclear.

Barring Americans from stepping foot in North Korea would mark the latest US step to isolate the furtive, nuclear-armed nation, and protect US citizens who may be allured by the prospect of traveling there. Nearly all Americans who have gone to North Korea have left without incident. But some have been seized and given draconian sentences for seemingly minor offenses.

The US government strongly warns Americans against traveling to North Korea, but does not prohibit it, despite other sanctions targeting the country. It is unclear exactly how many Americans go to North Korea every year. Those who typically do travel from China, where tour groups market trips to adventure seekers.

Some of those companies -- including China-based Young Pioneer Tours, which took Warmbier to Pyongyang -- have now stopped taking Americans. Other travel companies say they’re considering a similar restriction.

The US and North Korea have no diplomatic relations. The US has been pressing Pyongyang to halt its nuclear weapons development and urging China and other countries to starve the North of funding for the program. But on Tuesday, Trump suggested that strategy had failed.

“While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out,” Trump wrote on Twitter. “At least I know China tried!”

In Congress, Democrats and Republicans found rare bipartisan consensus in denouncing the North. Several senators said they were considering a travel ban. In the House, lawmakers lined up behind legislation from Rep. Adam Schiff, a Democrat, and Rep. Joe Wilson, a Republican.

Under their proposal, the Treasury Department would be ordered to prohibit all financial transactions related to travel to North Korea by Americans, unless specifically authorized by a US license. No licenses would be issued for tourism.

The Trump administration does not need an act of Congress to bar Americans from traveling to North Korea.

Under existing law, all it would take is a designation by Tillerson -- called a “geographic travel restriction” -- to make all American passports invalid for travel to North Korea. To back up the designation, Tillerson could assert that Americans face “imminent danger” to their health or safety if they travel there, an easily defendable assertion in the wake of Warmbier’s death.

The US does not currently prohibit its passports from being used to travel to any countries, even though financial restrictions limit US travel to Cuba and elsewhere. If a passport ban were placed on North Korea, an American who violated it could face a fine and up to 10 years in prison for a first offense.

Schiff said a new law was important to show Congress’ unity on North Korea, arguing that financial measures through the Treasury Department might be more effective than a passport ban because it would deter travel companies ferrying American.

“This has the merits of protecting Americans from going to a place of increasing danger, but also drying up one source of our currency for North Korea,” Schiff said in an interview.

Short of a total ban, Republican Sen. John McCain of Arizona proposed that prospective American travelers complete a form declaring they would not hold the US government responsible for what happens. He said the form would require Americans to affirm they are aware of what has transpired with other US citizens, such as Warmbier, whom the senator said was “murdered” by the North.

“If people are that stupid that they still want to go to that country, then at least they assume the responsibility for their welfare,” McCain said.