North Korea's official Korean Central News Agency called the launch a new type of "medium long-range" ballistic rocket that can carry a heavy nuclear war head.
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.
North Korea has been developing a long-range missile capable of striking the mainland United States mounted with a nuclear warhead.
"The test firing of ICBMs will occur at any time and place, at the will of North Korea's highest leadership", Ji said. However, Russia said it fell 310 miles (500 kilometers) from its coast.
"This is the longest-range missile North Korea has ever tested", Jeffrey Lewis of the Middlebury Institute of International Studies told AFP.
Kim said North Korea would stage more nuclear and missile tests in order to flawless nuclear bombs needed to deal with U.S.
"Successive administrations over 25 years have attempted to engage China unsuccessfully, but, for the first time, the Chinese appear to be focused on containing the nuclear ambitions of North Korea, so I think the [Trump] administration is pursuing a correct strategy", Faso said.
"The members of the Security Council agreed that the Security Council would continue to closely monitor the situation and take further significant measures including sanctions, in line with the Council's previously expressed determination", the Security Council said.
The launch jeopardises new South Korean president Moon Jae-in's willingness to talk to the North, and came as US, Japanese and European navies gather for joint war games in the Pacific.
The defense ministers of Japan and South Korea affirmed Monday that they will work closely with each other and with the United States following North Korea's latest ballistic missile launch the previous day, the Japanese Defense Ministry said.
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Lee Dong-ryul, from South Korea's Dongduk Women's University, said that as China's influence on North Korea shrank, one of the few effective measures left in Beijing's toolkit was cutting off its oil supply to North Korea.
What has North Korea been saying?
"If the USA awkwardly attempts to provoke the DPRK, it will not escape from the biggest disaster in the history, Kim said, strongly warning the United States should not to disregard or misjudge the reality that its mainland and Pacific operation region are in the DPRK's sighting range for strike and that it has all powerful means for retaliatory strike", KCNA said.
He said the missile's trajectory indicated the North was clearly testing the re-entry technology under flight environments that would be consistent for an ICBM.
There's also a political victory for North Korea.
John Schilling, a North Korean analyst, wrote on 38 North that the regime's successful missile test represented a level of performance "never before seen" from a North Korean missile, adding that it would have flown a distance of some 4,500 kilometers if launched at a flatter trajectory, which would place all of South Korea, Japan and US military bases in Guam within its reach.
Moon kept open the possibility of an inter-Korea summit, initially proposed last Wednesday in his inaugural speech, but said it can only be held when Pyongyang "changes its behavior".
On Monday, Russian President Vladimir Putin condemned the launch as "counterproductive, damaging, dangerous".
Jin Meihua, from the Northeast Asia Research Centre in Jilin province, said: "North Korea must have somehow prepared for possible further sanctions before this latest test".