Taken literally, such a policy would be tantamount to demanding a stoppage of any Chinese oil to North Korea, essentially an attempt to freeze out the country this winter and bring whatever industry it has to a halt.
The Chinese would almost certainly balk; they have never been willing to take steps that might lead to the collapse of the North Korean regime, no matter how dangerous its behavior, for fear that South Korean and American troops would occupy the country and move directly to the Chinese border.
Beyond that, the economic disruption of ending all trade with China would be so huge inside the United States that Mr. Trump’s aides declined on Sunday to discuss the implications.
After meeting with Mr. Trump, Defense Secretary Jim Mattis emerged to warn North Korea that “any threat to the United States or its territory, including Guam or our allies, will be met with a massive military response.” But Mr. Mattis, in a terse statement delivered on the White House driveway with the chairman of the Joint Chiefs of Staff, Gen. Joseph F. Dunford Jr., also offered a word of reassurance to the North’s reclusive leader, Kim Jong-un.
“We are not looking to the total annihilation of a country, namely North Korea,” he said. “But as I said, we have many options to do so.”
The statement echoed past comments by the defense secretary as well as a warning issued by President George W. Bush after North Korea’s first atomic test, in 2006. In that statement, Mr. Bush also said North Korea would be held responsible if it ever exported any of its nuclear weapons technology to other nations or to terrorists.
Still, Mr. Mattis’s statement left open many questions. His formulation seemed to rule out the kind of “preventive war’’ that the national security adviser, Lt. Gen. H. R. McMaster, warned last month might be necessary after the North tested two intercontinental ballistic missiles in an effort to demonstrate that it could reach Los Angeles and beyond. Instead, Mr. Mattis seemed to be talking about “pre-emptive strikes,” which the United States might order if it determined that an attack seemed imminent.
There was no public discussion of pursuing a diplomatic opening to the North. Mr. Trump and Secretary of State Rex W. Tillerson raised such a possibility two weeks ago, after a brief lull in North Korea’s testing. That statement turned out to be optimistic at best. The North has shown no interest in engaging with the United States unless the Americans end their military presence in the South.
To the contrary, the North Korean leader has tried to portray his nuclear program as unstoppable and nonnegotiable, posing by a picture of what the North’s official news agency on Sunday called a hydrogen bomb that could be fitted into the nose cone of the ICBMs tested last month. Experts warned that the weapon, while shaped like a hydrogen bomb, could well have been a mock-up or decoy, one of the many steps the North takes to make it appear more powerful than it truly is.
On Monday, South Korea’s army fired short-range ballistic missiles off its east coast in a simulated attack on North Korea’s nuclear test site, its military said in a statement. F-15K fighter jets also joined in the show of force, firing air-to-land missiles, it said.
Only hours earlier, Mr. Trump reacted to the North Korean test by lashing out at South Korea.
“North Korea is a rogue nation which has become a great threat and embarrassment to China, which is trying to help but with little success,” he said. “South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!”
Mr. Trump appeared to be referring to the offers by South Korea’s new president, Moon Jae-in, to enter into some kind of negotiations with the North that might lead to a renewal of the “Sunshine Policy,” an effort by some of his predecessors to lure the North into disarmament with economic engagement. Those efforts failed.
Mr. Moon said recently that he had obtained a promise from Washington that the United States would never take military action without Seoul’s approval — a commitment the Trump administration has never confirmed.
Mr. Trump’s undisguised swipe at the South for “appeasement” was certain to exacerbate fears that the United States might put it in danger. And it came only a day after Mr. Trump threatened a new rift in relations with suggestions that the United States might withdraw from a trade deal with South Korea — one that was intended to bolster the alliance.
In response to Mr. Trump’s criticism, Mr. Moon’s office said it was working closely with Washington to exert “maximum sanctions and pressure.” But it also reiterated that the allies shared the understanding that the goal of these sanctions and pressure was to bring North Korea back to the negotiating table.
“We have experienced an internecine war and can never tolerate another catastrophic war on this land,” Mr. Moon’s office said in a statement. “We will not give up our goal of working together with allies to seek a peaceful denuclearization of the Korean Peninsula.”
While Washington and Seoul argue over the threat of military force, Mr. Kim seems determined to forge ahead. He has conducted more than 80 missile tests since taking over the country. And four of the six nuclear tests have been on his watch.
This was the biggest, by far. The United States Geological Survey estimated that the tremor set off by the blast, detected at 12:36 p.m. at the Punggye-ri underground test site in northwestern North Korea, had a magnitude of 6.3.
The South Korean Defense Ministry’s estimate was much lower, at 5.7, but even that would mean a blast “five to six times” as powerful as the North’s last nuclear test, a year ago, said Lee Mi-sun, a senior analyst at the South Korean Meteorological Administration.
The South’s National Fire Agency, which operates an emergency hotline, said it had received 31 calls about buildings and the ground shaking, the first time that South Koreans had reported tremors after a North Korean nuclear detonation.
The blast was so powerful that the first tremor was followed by a second, weaker one minutes later, which the United States Geological Survey called a “collapse,” probably a cave-in at the North’s underground test site.
Condemnation of the test came from around the world.
China, the North’s main ally and biggest trading partner, expressed “strong condemnation” of the test, according to Xinhua, the state news agency, but suggested no new action. Its leaders feel as stymied as their American counterparts, according to many China experts.
The test’s timing was a major embarrassment for President Xi Jinping of China, who on Sunday was hosting a summit meeting of the so-called BRICS countries — Brazil, Russia, India, China and South Africa.
Peter Hayes, director of the Nautilus Institute, a United States-based research group specializing in North Korea, said the test seemed intended to jolt Mr. Xi and convince him that he needed to persuade the United States to talk to North Korea.
Japan requested an emergency meeting of the United Nations Security Council, as it did earlier in the week after a missile test over Hokkaido, its northernmost island.
In Europe, the Russian Foreign Ministry said that North Korea “deserves absolute condemnation,” and a joint statement from Chancellor Angela Merkel of Germany and President Emmanuel Macron of France said “the most recent provocation from Pyongyang reaches a new dimension.”
The International Atomic Energy Agency said the test amounted to a “complete disregard of the repeated demands of the international community.”
The timing of the test on Sunday was almost certainly no coincidence: It came during the American Labor Day weekend, and the anniversary of the founding of the North Korean government is next Saturday.
In the coming days, the government is expected to organize huge rallies to celebrate the bomb test and Mr. Kim’s leadership.
“Pyongyang has a playbook of strategic provocations, throws off its adversaries through graduated escalation, and seeks maximum political impact by conducting weapons tests on major holidays,” said Lee Sung-yoon, a Korea expert at the Fletcher School of Law and Diplomacy at Tufts University.
But it also exaggerates its power. After its fourth nuclear test, in January 2016, North Korea claimed to have used a hydrogen bomb. Other countries dismissed the claim for lack of evidence, but experts have said that the North may have tested a “boosted” atomic bomb that used tritium, a common enhancement technique that produces a higher explosive yield.
Analysts noted that the device in the photo that the North released on Sunday — whether real or a mock-up — was shaped like a two-stage thermonuclear device. David Albright, president of the Washington-based Institute for Science and International Security, said he doubted the device was real, but he said there was strong evidence that the North had been working on thermonuclear weapons.
“The size of the seismic signal of the recent test suggests a significantly higher explosive yield than the fifth test,” Mr. Albright said. “Getting this high of a yield would likely require thermonuclear material in the device.” But he said he was “skeptical that this design has been miniaturized to fit reliably on a ballistic missile.”