North Korea's official Korean Central News Agency said the country tested a new type of long-range missile "capable of carrying a large-size heavy nuclear warhead".
Outsiders also see a significant technological jump, with Sunday's test-fire apparently flying higher and for a longer time period than any other such previous missile.
Kim accused the United States of "browbeating" countries that "have no nukes" and warned Washington not to misjudge the reality that its mainland is in the North's "sighting range for strike", the North's official KCNA news agency reported.
Analysts have said the North learns something from each effort and appears to be making faster-than-anticipated progress toward its stated goal of developing a nuclear-tipped weapon that could target the US mainland. North Korea's push to boost its weapons programme also makes it one of the Trump administration's most urgent foreign policy worries.
Could North Korea launch a nuclear missile?
The country's leader, Kim Jong Un, supervised the launch of the Hwasong-12 missile that reached an altitude of 2,111.5 kilometers (1,312 miles) and flew 787 kilometers (489 miles), KCNA said.
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 kilometers (about 2,800 miles) if flown on a standard, instead of lofted, trajectory - considerably longer than North Korea's current missiles.
Japanese officials said the missile flew for about 800 kilometers before landing in the Sea of Japan.
However, the U.S. military's Pacific Command said on Sunday the type of missile that was sacked was "not consistent" with an ICBM and South Korea's military played down the North's claim of technical progress on atmospheric re-entry.
"I want to confirm that we are categorically against the expansion of the club of nuclear powers, including with the Korean peninsula and North Korea", said Putin, who said any such move would be "harmful and dangerous".
Japanese Defense Minister Tomomi Inada said the altitude and duration of the flight indicate it may have been a "new type of missile" but more analysis was needed.More news: Reliance Jio Broadband & More Awaited Jio Services in 2017
But experts immediately cast doubt on those claims, saying the missile's range looks long enough to reach U.S. military bases as far as Guam, a U.S. territory in the Western Pacific, but not as far as the U.S. West Coast.
"As we've spoken about with regards to China, North Korea is a liability for China, not an asset and China will partner with us to demonstrate to North Korea that it stands alone in its pursuit of illegal weapons of mass destruction", he said.
It says the "era of strategic patience" with North Korea is over.
"If the United States awkwardly attempts to provoke the DPRK, it will not escape from the biggest disaster in [.] history", KCNA quoted Kim as saying, referring to the North's formal name of the Democratic People's Republic of Korea.
There's also a political victory for North Korea.
The 38 North analysis points out that the distance flown by the missile means it could strike a US military base at Guam. "North Korea openly states that its ballistic missiles are meant to deliver nuclear weapons to strike cities in the U.S., the ROK, and Japan", Davis said.
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.
While Trump has said he'd be "honored" to talk with leader Kim under favorable conditions, Haley seemed to rule out the possibility.
"Let this latest provocation serve as a call for all nations to implement far stronger sanctions against North Korea", said the statement from White House press secretary Sean Spicer.
The South Korean military is gathering and analyzing information.