But since then, North Korea carried out one of its most provocative missile tests in recent years, hurling a ballistic missile directly over Japan that prompted the government in Tokyo to warn residents in its path to take cover. And on Sunday, the North conducted its most powerful nuclear test ever, with a blast that experts said was far more destructive than the bombs that the United States dropped on the Japanese cities of Hiroshima and Nagasaki during World War II.
In her remarks, Ms. Haley gave a lengthy summary of the North’s flouting of international law since 1993, when the United Nations urged the country to reconsider its decision to withdraw from the Nuclear Nonproliferation Treaty.
“Despite our efforts over the past 24 years, the North Korean nuclear program is more advanced and more dangerous than ever,” she said. “They now fire missiles over Japanese airspace.”
“They now have I.C.B.M. capabilities,” she said, referring to intercontinental ballistic missiles. “They now claim to have tested a hydrogen bomb. And just this morning there are reports that the regime is preparing for yet another I.C.B.M. launch.”
“We have taken an incremental approach,” Ms. Haley added, “and despite the best of intentions, it has not worked.”
Koro Bessho, the Japanese ambassador to the United Nations, also stopped short of threatening imminent military action, but said the danger from North Korea had been “raised to an unprecedented level” and was “a grave threat to the peace and the security of the world.”
Cho Tae-yul, the South Korean ambassador, called the North’s sixth and latest test its “most dangerous yet,” describing it as “do-or-die behavior.” He called for “truly biting and robust measures that Pyongyang finds really painful,” including blocking the flow of any money that might finance the North’s weapons program.
François Delattre, the French ambassador, also called for new sanctions. “It is no longer a regional threat, it is a global threat,” he said. “It is no longer a virtual threat, it is an imminent threat. It is no longer a serious threat, it is an existential threat.”
Liu Jieyi, the Chinese ambassador, vowed that Beijing would “never allow chaos and war” on the Korean Peninsula, where the United States and China were both combatants in a conflict that lasted from 1950 to 1953. He called for all sides to return to the negotiating table, as did Vasily A. Nebenzya, the Russian ambassador.
The warning by South Korean officials on Monday that the North may be making preparations to launch another ballistic missile did not make clear exactly what sort of missile that might be.
The North first tested its new intercontinental ballistic missile Hwasong-14 on July 4, and again on July 28. The second test showed the missile had a range of about 6,500 miles, which would put the western and central United States within range.
The nuclear test the North carried out on Sunday triggered a magnitude 6.3 tremor centered at the testing site in the country’s northeast, the United States Geological Survey said. It was followed by a weaker tremor believed to have been the result of a collapse in the testing site.
President Trump said on Twitter that Sunday’s test was an “embarrassment” to China, the North’s biggest ally and trade partner. He also criticized South Korea, an American ally, which he accused of “talk of appeasement.”
Then on Monday, the South Korean military carried out drills, with F-15K fighter jets and ground forces firing missiles in a simulated attack on the North’s nuclear site.
The South Korean president, Moon Jae-in, talked with the American president on the phone on Monday evening, his office said.
”President Trump reaffirmed the United States’ ironclad commitment to defend South Korea,” said Park Soo-hyun, a spokesman for Mr. Moon. “The two leaders also agreed to push for maximum pressure and sanctions against North Korea and a stronger sanctions resolution at the United Nations Security Council.”
During the call, the spokesman said, Mr. Trump resolved a major South Korean grievance by agreeing to let it build more powerful non-nuclear ballistic missiles.
Under a treaty with the United States that was aimed at preventing a regional arms race, South Korea has been able to build ballistic missiles only with a range of up to 497 miles. But those missiles’ payload could not exceed 500 kilograms, about half a ton.
On Monday, Mr. Trump agreed to lift the upper limit on the payload, Mr. Park said. Mr. Moon agreed to help the United States complete the deployment of the Thaad missile-defense system as soon as possible.
Testifying before the National Assembly on Monday, Defense Minister Song Young-moo of South Korea said he told his American counterpart, Jim Mattis, in a meeting last week that the United States needed to send long-range bombers, aircraft carriers and other strategic assets to the Korean Peninsula more often or regularly to reassure the South Koreans.
He said he told Mr. Mattis that many in South Korea were calling for the reintroduction of American tactical nuclear weapons to South Korea. He did not disclose how Mr. Mattis responded.
President Moon’s office said his government remained opposed to the introduction of American tactical nuclear weapons to South Korea.
After North Korea’s intercontinental ballistic missile tests in July, South Korea’s main conservative opposition party and some domestic news media called for the United States to redeploy tactical nuclear weapons to South Korea. Recent surveys have also shown that a majority of South Koreans agree or support arming their country with nuclear weapons of its own.
But the government says that it would make it more difficult to persuade North Korea to give up its own nuclear weapons.
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