Thursday's launch was the first full ICBM test by nuclear-armed North Korea since 2017.
Flight data indicated the missile flew higher and longer than any of North Korea's previous tests before crashing into the sea west of Japan.
What North Korea calls the Hwasong-17 would be the largest liquid-fuelled missile ever launched by any country from a road-mobile launcher, analysts say.
Its range and size suggest North Korea plans to tip it with multiple warheads that could hit several targets or with decoys to confuse missile defences, they say.
The leaders of the G7 countries and the European Union condemned North Korea's test as a "reckless" threat to peace and security and a danger to international civil aviation and maritime navigation.
They said it demanded a united response.
North Korea's last ICBM launches in 2017 prompted United Nations Security Council sanctions but council members are at odds over the Ukraine war, making such a response more difficult.
The Security Souncil is due to meet to discuss the launch later on Friday at the request of the United States and allies.
On Thursday, Secretary-General Antonio Guterres urged North Korea "to desist from taking any further counter-productive actions".
Russia's RIA news agency quoted the Russian foreign ministry as saying that Russia and China had agreed to co-ordinate closely on the situation on the Korean peninsula.
"Concern was expressed over the latest developments in the sub-region" at a meeting between Russian Deputy Foreign Minister Igor Morgulov and China's representative for the Korean Peninsula, it said, adding that they emphasised the need to step up efforts towards fair political and diplomatic solutions for the problems of northeast Asia.
North Korean state media said Kim ordered the test because of "daily-escalating military tension in and around the Korean peninsula" and the "inevitability of the long-standing confrontation with the US imperialists accompanied by the danger of a nuclear war".
"The strategic forces... are fully ready to thoroughly curb and contain any dangerous military attempts of the US imperialists," Kim said while overseeing the launch.
It comes after the election of a new conservative South Korean administration that has pledged a more muscular military strategy towards North Korea.
President-elect Yoon Suk-yeol said North Korea had nothing to gain from provocation.
In a call with Chinese President Xi Jinping after the launch, Yoon called for close co-ordination on North Korea's complete denuclearisation, his office said.
Xi said China and South Korea should bolster mutual political trust, Chinese state media said.
China, North Korea's sole major ally and neighbour, urged restraint on "all sides" after the test.
Kim said the test would help convince the world of the power of his strategic forces.
"Any forces should be made to be well aware of the fact that they will have to pay a very dear price before daring to attempt to infringe upon the security of our country," he said.
North Korean state media showed a massive missile, painted black with a white nose cone, rising on a column of flame from a launch vehicle.
It said the Hwasong-17 flew for 1090km to an altitude of 6,248.5km and hit a target in the sea, similar numbers to those reported by Japan and South Korea.
Kim, who the state broadcaster showed in video at the launch site dressed in a leather jacket and sunglasses, called it a "miraculous" and "priceless" victory for the Korean people.
