Here in Seoul, the Defense Ministry warned that Pyongyang might be preparing to launch another missile into the Pacific Ocean, perhaps an intercontinental ballistic missile theoretically capable of reaching the mainland United States.
President Trump and his South Korean counterpart, Moon Jae-in, spoke on the phone for 40 minutes Monday night, Korean time — some 34 hours after the nuclear test and more than 24 hours after Trump took to Twitter to criticize Moon's "talk of appeasement."
The two agreed to remove the limit on allowed payloads for South Korean missiles — something Seoul had been pushing for — as a way to increase deterrence against North Korea, according to a statement from South Korea's Blue House.
They agreed as well to work together to punish North Korea for Sunday's nuclear test, pledging "to strengthen joint military capabilities," a White House statement said, and to "maximize pressure on North Korea using all means at their disposal."
In a later phone call, Trump and German Chancellor Angela Merkel "reaffirmed" the necessity of coordinating a response at the United Nations.
At a U.N. Security Council meeting, Haley pressed for the "strongest possible" sanctions against the North. The administration plans to circulate a new sanctions draft this week. Haley did not spell out how she would overcome the objections of veto-wielding permanent members China and Russia.
But she cautioned, "War is never something the United States wants. We don't want it now. But our country's patience is not unlimited. We will defend our allies and our territory."
Haley ruled out the "freeze for freeze" proposal backed by China and Russia, which would suspend U.S. joint military exercises with South Korea in return for suspension of North Korean nuclear and missile tests.
"When a rogue regime has a nuclear weapon and an ICBM pointed at you, you do not take steps to lower your guard. No one would do that. We certainly won't," she said.
Instead, she reiterated a White House threat from Sunday to cut off trade with any countries that also trade with North Korea. That would presumably include China, with which the United States had nearly $650 billion worth of trade in goods and services last year.
"The United States will look at every country that does business with North Korea as a country that is giving aid to their reckless and dangerous nuclear intentions," she said.
Her remarks appeared to be unpersuasive. "China will never allow chaos and war" in Korea, said Liu Jieyi, the Chinese ambassador to the United Nations. Sanctions alone will not solve the crisis, said Russia's U.N. ambassador, Vassily Nebenzia.
Earlier Monday, South Korean Defense Minister Song Young-moo said that he asked his American counterpart, Jim Mattis, during talks at the Pentagon last week that strategic assets such as U.S. aircraft carriers, nuclear submarines and B-52 bombers be sent to South Korea more regularly.
"I told him that it would be good for strategic assets to be sent regularly to the Korean Peninsula and that some South Korean lawmakers and media are strongly pushing for tactical nuclear weapons [to be redeployed]," Song told a parliamentary hearing on North Korea's nuclear test, without disclosing Mattis's response.
A poll that YTN, a cable news channel, commissioned in August found that 68 percent of respondents said they supported bringing tactical nuclear weapons back to South Korea.
"The redeployment of tactical nuclear weapons is an alternative worth a full review," Song said, echoing a position closely associated with conservatives in South Korea but not with progressives like Moon, who was elected president in May after vowing to engage with the North.
The United States had about 100 nuclear-armed weapons, including short-range artillery, stationed in South Korea until 1991. Then President George H.W. Bush signed the Presidential Nuclear Initiatives and withdrew all tactical nuclear weapons that had been deployed abroad.
Shortly afterward, the two Koreas signed an agreement committing to making the peninsula free of nuclear weapons — a deal that North Korea violated by developing its own nuclear arms. But Pyongyang has maintained that Seoul has also broken its promise because remaining under the U.S. nuclear umbrella is tantamount, it says, to having such weapons.
After the defense minister spoke at the hearing, the South Korean president's office said that it was not considering redeploying tactical nuclear weapons. "Our government's firm stance on the nuclear-free peninsula remains unchanged," said Kim Dong-jo, a spokesman for Moon.
Military experts in the United States are almost universally opposed to the idea of deploying strategic or tactical weapons in South Korea.
"The thing that most concerns me about redeployment is that it introduces more room for miscalculation or unintended escalation," said Catherine Dill of the Center for Nonproliferation Studies in Monterey, Calif.
In that situation, the ability to react more quickly could be a negative factor.
From the perspective of the military alliance between the United States and South Korea, having long-range ballistic missiles or strategic bombers is "perfectly sufficient" to continue to deter North Korea, Dill said.
As alliance partners, the U.S. and South Korean militaries work in close cooperation, regularly conducting drills together. This includes sending "strategic assets" such as bombers stationed on the Pacific island of Guam over South Korea on a regular basis, and having submarines make port calls during exercises.
As the North Korean threat has increased this year, the United States has sent F-35 stealth aircraft and other strike fighters on flyovers across the southern half of the peninsula in a not-so-thinly veiled warning to Kim. The U.S. Pacific Command even released photos last week of B-1B Lancers dropping bombs on a range on the southern side of the demilitarized zone that separates the two Koreas.
But a growing number of policymakers in Seoul say that Guam is too far away and that, if the South comes under attack from North Korea, it can't wait the two-plus hours it would take American bombers to arrive from their base in the Pacific.
"We need these strategic or tactical assets that can destroy North Korea's nuclear-capable missiles before they can inflict harm on us," said Chun Yung-woo, a former South Korean national security adviser.
"Right now they can retaliate, but by that time, tens of thousands of people might have been killed," Chun said. "We need a first layer of offensive weapons stationed closer to North Korea's nuclear and missile sites."
Jon Wolfsthal, a nuclear expert who served on President Barack Obama's National Security Council, said that in the South Korean context, "strategic assets" are all about giving "a tangible sense of reassurance" to the government in Seoul.
"The reassurance bucket is bottomless," Wolfsthal said. "You can pour stuff into it and it's never going to fill up."
South Korean officials have been asking for fighter jets and ballistic missile-equipped submarines to be based on the peninsula, and have long wanted B-1Bs and B-52s to land rather than just fly over — all to give a greater sense of U.S. commitment to South Korea.
But there are good logistical reasons that can't happen, Wolfsthal said. For one, South Korea doesn't have airstrips long enough for big, heavy B-52s, and second, the United States does not want its high-tech fighter jets sitting within North Korean artillery range.
South Korea has been flexing its military muscles in response to North Korea's provocations, practicing at dawn Monday for strikes on the North Korean nuclear test site at Punggye-ri.
The South Korean air force will stage a live-fire drill, launching Taurus air-to-surface guided missiles from F-15K fighter jets, later this month, the Defense Ministry said Monday. The missiles have a range of 300 miles — enough to carry out precision strikes on North Korea's key nuclear and missile sites.
The ministry also said it had seen signs of preparation for another North Korean ballistic missile launch, and South Korea's national intelligence service told lawmakers that it could be another intercontinental ballistic missile.
Yoonjung Seo in Seoul and Anne Gearan in Washington contributed
to this report.