U.S. President Donald Trump is facing some grim math. With one American declared dead after being released from a prison in North Korea and three still in captivity there, he'll have to reckon with how to respond to a regime once dubbed by former U.S. official Victor Cha as "the land of lousy options."

Otto Warmbier, 22, died at home on Monday, just days after being "medically evacuated" in a coma following 17 months of detention in North Korea. Warmbier, a tourist at the time, was detained in 2015 and convicted of "hostile acts" for allegedly taking down a propaganda poster. He was sentenced to 15 years of hard labour.

Offering condolences on Monday, the president vowed "to handle" the isolated communist nation. But experts say Trump, who in April advocated for a new North Korean strategy of "maximum pressure and engagement," might now be tempted to reconsider taking a tougher line on Pyongyang following the loss of an American life.

Not many viable choices

Military action that could amount to war on the Korean Peninsula would be potentially catastrophic for Japan and South Korea, so the viable choices on the table fall into a familiar diplomatic rut: Tightening economic sanctions, threatening to put North Korea back on a list of state sponsors of terrorism and trying to ban travel to North Korea via executive order or through Congress.

In this Feb. 29, 2016, photo, American student Otto Warmbier cries while speaking to reporters in Pyongyang, North Korea. Warmbier died days after being released from North Korea in a coma. (Korean Central News Agency/Korea News Service via AP)

Chinese officials will visit the White House on Wednesday, at which time Trump is expected to press them on North Korea and on enforcing sanctions on the regime of Kim Jong-un.

Mostly, though, the prospect of pressuring other countries to impose sanctions doesn't depart dramatically from the Obama-era policy of "strategic patience," says Jordan Tama, a former fellow with the Wilson Centre's Asia Program and an associate professor of foreign policy at American University in Washington, D.C.

What sanctions are left?

"So many sanctions" have already been slapped on North Korea, Tama says, that "it can be hard to come up with additional ways to punish the government for bad behaviour."

Congressional Republicans outraged by Warmbier's death accused Kim's authoritarian government of murder. Trump called the death a "disgrace," slamming North Korea as a "brutal regime."

Even so, escalation of an already tense situation could further endanger Americans, making it "akin to a hostage situation," Tama warns.

The Trump administration's willingness to follow through with exerting "maximum pressure" could be limited by Kim Dong-chul, Tony Kim and Kim Hak-song, the three U.S. citizens still detained in North Korea.

"The real challenge here is you don't want to jeopardize their lives by pushing too hard," says Celeste Arrington, a foreign policy expert with George Washington University who has extensively researched abductions of foreign nationals in North Korea.

There are not signs North Korea wants to pursue any kind of constructive engagement - Celeste Arrington, George Washington University

Tama says that while "it wouldn't be right" for the U.S. to refrain from pressuring North Korea because it has Americans in detention, the White House will have to bear in mind the risks involved.

Pyongyang has already demonstrated its willingness to be provocative and take "rash actions," so "there's always the chance they could cause harm to other American detainees," Tama says.

"But you also don't want to allow for blackmail … by giving North Korea an incentive to detain Americans in order to prevent us from carrying out policies North Korea wouldn't like."

Vow to hold North Korea 'accountable'

For her part, Arrington doubts Warmbier's death will change foreign policy toward North Korea in any major way. The government continues to test nuclear weapons and reject humanitarian assistance from South Korea, for example.

"There are not signs North Korea wants to pursue any kind of constructive engagement."

In a statement demanding the release of the remaining three Americans, Secretary of State Rex Tillerson said on Monday the U.S. would "hold North Korea accountable" for Warmbier's fate.

Arrington says that statement lacked teeth, noting that hundreds of Japanese, South Korean and Chinese nationals are believed to have been detained by the government, including Canadian pastor Hyeon Soo Lim, who remains in captivity.

"And yet we've seen no accountability so far," Arrington says. "It's shocking because Mr. Warmbier was so young, but this is just the tip of the iceberg."

The U.S. government continues pressing for the safe return of the three Americans still in North Korea, all of whom are of South Korean ancestry.

Until Warmbier's death, it was believed Korean-American detainees were subjected to harsher treatment than white Americans, says Olivia Enos, policy analyst in the Asian Studies Centre at the Heritage Foundation in Washington. That theory appears to have been debunked by Warmbier's fate.

"North Korea has literally gone and killed a U.S. citizen," Enos says, echoing accusations of murder by some congressional Republicans.

Condemnation building on Capitol Hill

With that in mind, she believes there's more of an impetus "to get tougher on North Korea" to follow through with the U.S. government's duty to protect the rights and lives of Americans.

She wants to see the White House seek enforcement of a North Korea travel ban for Americans, a move supported by Anthony Ruggiero, a former U.S. official in the State and Treasury departments.

"My expectation is there will be condemnation on Capitol Hill, building on prohibiting some form of travel to North Korea. The next step is for Congress to act."

Secretary of State Rex Tillerson says the U.S. would 'hold North Korea accountable' for Warmbier's death. (The Associated Press)

Tillerson has suggested he's considering a ban on American travel, or putting a visa restriction in place, as the department warns citizens of the severe risk.

Restricting travel means fewer hostages

Ruggiero, now a senior fellow with the Foundation for Defence of Democracies specializing in North Korea, says restricting travel would limit North Korea's ability to detain Americans "for use as bargaining chips" in negotiations in which the regime dictates the terms.

"It's not a surprise," he says, "that two Americans taken last year were [detained] in the same time frame around North Korean provocations and sanctions were being considered" in the U.S. Congress and the United Nations.

About 1,000 Americans travel to North Korea each year, according to a report in the Wall Street Journal. The tour company Warmbier was travelling with when he was detained in North Korea, Young Pioneer, announced it would no longer be taking Americans to the country.

Ruggiero says the visit from top Chinese diplomats to Washington on Wednesday will include demands that Beijing ramp up efforts to put economic pressures on Pyongyang. Judging by Trump's tweet on Tuesday, the president doesn't sound confident he'll be able to convince them.