Can the two sides manage to sit down and thrash out their differences face to face?
After North Korea's shock demonstration that it can strike the American mainland with an intercontinental missile, US officials say their focus remains on finding a diplomatic solution to avert a catastrophic conflict.
But with Washington reluctant to be seen to be rewarding Pyongyang, whose leader Kim Jong-Un has been taunting the "American bastards", can the two sides manage to sit down and thrash out their differences face to face?
Analysts and diplomats who are veterans of previous flare-ups in tensions between the two countries acknowledge there are huge obstacles in the way of talks -- not least because they have no diplomatic relations.
But they also say talks are not only possible but really the only viable solution, whether talking directly or via third parties -- including senior US politicians outside the Trump administration.
"The only way out here is diplomacy," said James Clapper, who spent years as a US intelligence chief in South Korea and was later Director of National Intelligence under Barack Obama.
Donald Trump said in May that he would be "honored" to meet with Kim under what he called the right circumstances, in essence demanding North Korea first halts its nuclear and ballistic missile programs.
While the US president promised a "pretty severe" retort to North Korea's intercontinental ballistic missile (ICBM) test, his defense secretary Jim Mattis' response was to echo Britain's wartime leader Winston Churchill famous mantra that it is "better to jaw-jaw than war-war."
And Kim also appeared to leave the door open for talks after Tuesday's test, saying his nuclear and ballistic missile programs could be "on the table" if the US dropped what he called its "hostile policy".
While Pyongyang has been seeking to engage Washington in bilateral talks for decades, Washington has insisted on indirect and informal contacts.
Through the 2000s, a six-party format -- including China, Russia, Japan, and South Korea -- appeared to draw North Korea, then under Kim's father Kim Jong-il, toward some level of outside nuclear monitoring and a possible slowdown in their program.
But that process collapsed in 2009, and since gaining power two years later, Kim Jong-un has dismissed talks for his determination to achieve nuclear status, as much for his domestic political stature as demonstrating the country's military prowess.
Building trust
Since then, contacts have been through forums, seminars involving former officials, academics, humanitarian representatives and at times officials acting only in a semi-official capacity.
Such meetings can be turgid, with North Koreans reading off a playlist of positions believed dictated directly by Kim. It takes a lot of work to bridge language and cultural gaps, according to people who have participated.
Nevertheless, "there's an ability to build some trust," said Joseph DeTrani, a former State Department envoy to the six-party talks.
And in the past, when the US sought to get North Korea to free Americans detained as spies or illegal prosyletizers, Kim Jong-Il was willing to meet and deal with US emissaries like former presidents Bill Clinton and Jimmy Carter, and former UN ambassador Bill Richardson.
Such meetings have been rare under Kim Jong-Un but he did meet with former basketball star Dennis Rodman who has been a regular visitor to North Korea over the years.
"We had periods when there were agreements, that was with Kim Jong-il," said DeTrani who regards Kim Jong-UN as a more "reckless" leader.
Rather than using third parties, some voices are pushing for the US to establish semi-formal relations by setting up a North Korea Interests Section in Pyongyang, staffed by US diplomats, and allowing a North Korean counterpart in Washington.
But after a channel is opened, then what?
Iran talks a model?
Scott Snyder, a Korea expert at the Council on Foreign Relations, says the fundamental problem is that the US cannot accept North Korea's demand to back off its regional military stance protecting South Korea and Japan.
"The problem is where the North Koreans want to go with this is exactly the place where we don't want to go," he said.
Frank Aum, a former Defense Department official now with the US Korea-Institute at Baltimore's Johns Hopkins University, said the Trump administration had to adapt by accepting -- at least internally -- that it is effectively dealing with a nuclear power that needs to be contained.
Aum supports intensifying the existing approach of applying economic pressure on North Korea via sanctions and trying to get China to bring its influence to bear on Pyongyang -- arguing that such tactics helped persuade Iran to curb its nuclear program during Obama's presidency.
"It took three years for sanctions on Iran to begin working," he said.
The Trump administration though is no fan of the Iran nuclear deal, calling it one of the worst in history.
And Scott Snyder, a Korea expert at the Council on Foreign Relations, said the Iran model won't work because Pyongyang already has a proven nuclear capability and its leadership was much more immune to outside pressure.
"The regime benefits from political isolation," he said.
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