Her remark came a day after the North’s most powerful nuclear test, and hours after South Korean officials told lawmakers that North Korea may be making preparations to launch another ballistic missile to mark the anniversary of the founding of the North Korean government over the coming weekend.
“We have kicked the can down the road long enough,” Ms. Haley told the council in an emergency meeting. “There is no more road left.”
But Ms. Haley did not threaten unilateral military action by Washington, or repeat President Trump’s statement on Twitter that South Korea’s call for more diplomacy was a form of “appeasement.” Ms. Haley said instead that “the time has come for us to exhaust all of our diplomatic means before it’s too late.”
It was the second time in less than a week that the Security Council has met to discuss North Korea, and the 10th time it has done so this year. Last month, the council severely tightened sanctions against North Korea.
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. On Sunday, it conducted its most powerful nuclear test ever, with a blast that experts said was far more destructive than the bombs dropped on the Japanese cities of Hiroshima and Nagasaki during World War II.
In her speech, Ms. Haley ticked off a lengthy summary of the North’s flouting of international law since 1993, when the United Nations urged the North 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. 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,” she added, “and despite the best of intentions, it has not worked.”
Although experts do not agree on Mr. Kim’s precise motivations, Ms. Haley said “he wants to be acknowledged as a nuclear power,” which she said was unacceptable. “Being a nuclear power is not about using those terrible weapons to threaten others,” she said. “Nuclear powers understand their responsibility. Kim Jong-un shows no such understanding.”
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 “a grave threat to the peace and the security of the world.”
François Delattre, the French ambassador to the United Nations, called for the prompt adoption of new sanctions and said “the threat has changed in nature and dimension” over just the past few months.
“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.”
Matthew Rycroft, the British envoy to the United Nations, said sanctions against North Korea were working, making it harder for Pyongyang to acquire the hard currency needed to finance its weapons program.
But he said North Korea was “uniquely willing to put their illicit programs ahead of the well being of its people.”
Mr. Rycroft said the world remained open for North Korea to “return to dialogue.”
Liu Jieyi, the Chinese ambassador to the United Nations, vowed that Beijing “will never allow chaos and war” on the Korean Peninsula, where the United States and China were both combatants in a war that lasted from 1950 to 1953. He called for all sides to return to the negotiating table.
Like his Chinese counterpart, Vasily A. Nebenzya, the Russian ambassador to the United Nations, condemned North Korea in forceful terms, but also argued that there was no feasible military resolution.
Mr. Nebenzya urged “all stakeholders to return immediately to dialogue,” and said the impasse could be resolved “solely through diplomatic and political channels.”
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.
The South Korean military carried out drills Monday in response to the test, with F-15K fighter jets and ground forces firing missiles in a simulated attack on the North’s nuclear site.
The South Korean defense minister, Song Young-moo, said Monday that in recent talks he had asked the United States to deploy strategic assets, including an aircraft carrier group and bombers.
In South Korean officials’ warning that the North may be making preparations to launch another ballistic missile, it was not immediately clear exactly what sort of missile that might be. It first tested its new Hwasong-14 missile 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.
News of preparations for the test came as the South Korean Defense Ministry said the United States military would soon add four additional launchers for a missile defense system deployed in the country’s south.
President Trump said on Twitter that the test was an “embarrassment” to China, the North’s biggest ally and trade partner, and he criticized South Korea, an American ally, which he accused of “talk of appeasement.”
The office of South Korea’s president, Moon Jae-in, responded that it was working to exert “maximum sanctions and pressure” on the North and reiterated that its goal was “peaceful denuclearization of the Korean Peninsula.”
South Korea’s Ministry of the Environment also gave its preliminary approval Monday for the full deployment of a missile defense system operated by the United States.
Also on Monday, the South Korean News Agency Yonhap reported that the South Korean city of Incheon was canceling plans for a military re-enactment of the Sept. 15, 1950, landing there of American and allied forces led by Gen. Douglas MacArthur, which helped turn the tide of the Korean War. The event was called off because of the burden it would put on military forces during the current tensions, officials said.