The European Union also released a statement condemning Pyongyang's missile test as a threat to global peace and security, calling for North Korea to immediately stop its missile launches and abandon its weapons of mass destruction.
The rocket, "newly designed in a Korean-style", flew 490 miles and reached a maximum altitude of 1,310 miles, the North said, and "verified the homing feature of the warhead under the worst re-entry situation and accurate performance of detonation system".
The United States called the missile launch a message to South Korea, days after its new president took office pledging to engage Pyongyang in dialogue and keep up worldwide pressure to impede the North's arms pursuit.
The UN Security Council is scheduled to meet on Tuesday to discuss Sunday's missile launch. If launched on a maximum trajectory, the latest missile could have flown about 4,500 kilometres, within range of the U.S. military base at Guam, according to aerospace engineer John Schilling.
In a statement, White House spokesman Sean Spicer said the move should "serve as a call for all nations to implement far stronger sanctions against North Korea".
The news agency added that North Korean leader Kim Jong Un "personally oversaw" the missile test.
North Korean leader Kim Jong Un had hugged rocket research officials after witnessing the test, saying they worked hard to achieve a great thing, they said.
US Pacific Command said the projectile, which fell into the Sea of Japan, wasn't consistent with an ICBM and didn't pose a threat to North America.
The White House, in a statement, said that North Korea has been "a flagrant menace for far too long".
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In an official statement, North Korea warned the USA against reckless provocations because the US mainland and America's allies in the region are within the missile's range.
But, he added: "We must stop intimidating North Korea and find a peaceful solution to this problem".
The North Korean news agency KCNA has reported that Kim warned the United States should not misjudge the reality that its mainland is in the North's "sighting range for strike".
David Wright, co-director of the Global Security Program at the Union of Concerned Scientists, said the missile could have a range of 4,500 km (about 2,800 miles) if flown on a standard, instead of a lofted, trajectory - considerably longer than Pyongyang's current missiles.
"It appears to have not only demonstrated an intermediate-range ballistic missile (IRBM) that might enable them to reliably strike the US base at Guam, but more importantly, may represent a substantial advance to developing an intercontinental ballistic missile (ICBM)".
Moon, South Korea's first liberal leader in almost a decade, said as he took his oath of office last week that he'd be willing to visit North Korea if the circumstances were right.
The launch came as troops from the US, Japan and two European nations gather near Guam for drills that are partly a message to North Korea.
As Chinese President Xi Jinping prepared to inaugurate the Belt and Road Forum, Pyongyang fired a ballistic missile from a base in the country's northwest, near the border with China. The militaries of Japan and South Korean have increased their presence on the Korean peninsula.
North Korea, which is banned by U.N. resolutions from engaging in nuclear and missile developments, has accused the United States of a hostile policy to crush its regime, calling its nuclear weapons a "sacred sword" to protect itself.