SEOUL—North Korea said it successfully test-launched an intercontinental ballistic missile, claiming a major advance for the isolated nation in its attempts to threaten the U.S. with a nuclear weapon.

The announcement was made on North Korean state television on Tuesday afternoon—in the early hours of Independence Day in the U.S.

The missile, identified as the Hwasong-14, was launched at a steep trajectory and flew 933 kilometers (580 miles), reaching an altitude of 2,802 kilometers, according to North Korean state television. The numbers are in line with analyses from U.S., South Korean and Japanese military authorities.

North Korean leader Kim Jong Un said earlier this year that the country was close to test-launching an ICBM. U.S. President Donald Trump said on Twitter a day later: “It won’t happen!”

North Korea’s claim of an ICBM has the potential to change the strategic calculus between Washington and Pyongyang and across Northeast Asia, as Mr. Kim’s regime continues to defy United Nations sanctions and warnings from its neighbors to curb its nuclear and weapons programs.

Since the rise of Mr. Kim, the North’s third-generation leader, in 2011, Pyongyang has accelerated its missile-development program, adding new capabilities that have given it the ability to fire missiles farther and with less preparation time, making a potential launch more difficult to detect and stop.

The U.S. has weighed military options against North Korea since at least the early 1990s, but appears to have decided in each case that it was too risky. North Korea has amassed enough artillery across the demilitarized zone that divides the Korean Peninsula to bombard Seoul, the South Korean capital that sits just 35 miles south of the border. In addition, the U.S. has roughly 28,500 troops stationed in South Korea.

The claim of a working ICBM that could potentially put the continental U.S. in danger raises the stakes of any so-called military option against North Korea.

In a statement published hours after the missile launch by its official mouthpiece, the Korean Central News Agency, North Korea said that it was a nuclear power that possesses both nuclear bombs and ICBMs that were capable of ending what it called “the U.S. nuclear war threat.”

The missile that North Korea launched on Tuesday morning flew more than 580 miles, according to a spokesman for South Korea Ministry of National Defense.

But it was fired at a very steep trajectory, in line with some of the North’s recent launches—done in part to prevent its missiles from flying over neighboring countries like Japan.

The U.S. Pacific Command in Hawaii said the missile flew for 37 minutes—a relatively long period for such a short distance—before splashing down in the waters between Japan and Korea.

The statement from Pacific Command identified the missile as being an intermediate-range ballistic missile, which is generally defined as a missile with a range of between 3,000 and 5,500 kilometers.

If fired at a more standard trajectory, the missile that Pyongyang launched on Tuesday could have flown for more than 4,160 miles, said David Wright, a physicist at the Union of Concerned Scientists. That is far enough to qualify as an ICBM.

During an emergency meeting of South Korea’s National Security Council on Tuesday, President Moon Jae-in called for more U.N. Security Council measures against North Korea, while condemning the launch for coming just days after his meeting with Mr. Trump in Washington, where they urged North Korea to refrain from provocations.

The distinction between an intermediate-range and intercontinental ballistic missile is an important one because the U.S. has forbidden North Korea from conducting an ICBM test, though it is unclear what the U.S. would do in response to a possible declaration from Pyongyang of a successful ICBM test.

On Tuesday, before North Korea’s ICBM claim, Mr. Trump tweeted: “North Korea has just launched another missile. Does this guy have anything better to do with his life? Hard to believe that South Korea and Japan will put up with this much longer. Perhaps China will put a heavy move on North Korea and end this nonsense once and for all!”

At a regular briefing Tuesday, a spokesman from China’s Foreign Ministry reiterated Beijing’s position that it opposes any actions taken by North Korea that violate United Nations Security Council resolutions. On the issue of Mr. Trump’s tweets, Geng Shuang said China has worked tirelessly for stability on the Korean Peninsula.

“China’s efforts are obvious to all,” he added.

Satellite imagery released late last month by 38 North, a North Korea-focused blog published by the U.S.-Korea Institute at Johns Hopkins University’s School of Advanced International Studies, showed that North Korea had conducted a test of a rocket engine that some analysts believe could be used for an intercontinental ballistic missile.

Japanese government spokesman Yoshihide Suga said the latest missile appeared to land in Japan’s maritime exclusive economic zone, which extends about 200 nautical miles from the coast. Last year, North Korea fired four missiles that landed in Japan’s EEZ.

North Korea’s launch, which took place at 9:10 a.m. Pyongyang time from Banghyon, north of the capital, was first in more than a month.

North Korea has test-launched missiles on or around July 4 before, including in 2006 and 2009. The latest test follows Mr. Moon’s visit to the White House last week and comes ahead of this week’s Group of 20 summit in Germany, where Mr. Trump is expected to press Chinese leader Xi Jinping for more help in curtailing Pyongyang’s weapons program.

Japanese Prime Minister Shinzo Abe said Tuesday that he would seek coordination with other global leaders at the G-20 summit to respond to North Korea.

“This missile launch clearly shows the threat is increasing further,” Mr. Abe told reporters.

North Korea has accelerated its missile and nuclear-bomb testing under Mr. Kim, who took power at the end of 2011. So far this year, North Korea has launched 13 ballistic missiles, more than in any of the previous three years up to this time of the year, according to Shea Cotton, a research associate at the Middlebury Institute of International Studies in Monterey, Calif.

Its previous launch in early June, was with multiple cruise missiles rather than a ballistic missile, which leaves the atmosphere.

It last launched a ballistic missile in late May, into the waters between Japan and Korea.