Sunday's rocket took off at around 9am Pyongyang time from the North's west coast, according to South Korea's defence ministry.
:: Five Questions About North Korea's Rocket Launch
Japan's NHK broadcaster reported debris from the rocket was believed to have fallen about 155 miles (250km) off the southwest coast of the Korean Peninsula into the East China Sea about 14 minutes after the launch.
NHK also showed footage of an object visible in the skies from the southern island of Okinawa that was believed to be the rocket.
North Korea insists the planned launch is part of its space exploration programme - but most of the world views it as a disguised ballistic missile test.
The UN Security Council prohibits North Korea from nuclear and ballistic missile activity and is holding an emergency meeting in the next few hours to discuss the North's actions.
However, Pyongyang remained defiant hours after the launch, with its embassy in Moscow issuing a statement saying it would "continue to launch more man-made satellites".
Britain - and both US Secretary of State John Kerry and Japanese Prime Minister Shinzo Abe - condemned the launch as "a violation" of UN Security Council resolutions.
Mr Kerry said it was the second time in just over a month that North Korea has chosen to conduct "a major provocation, threatening not only the security of the Korean Peninsula, but that of the region and the United States as well".
Even the isolated state's sole major ally China expressed "regret".
Russia too, considered an ally of North Korea, slammed the launch, saying Pyongyang had once again demonstrated a disregard for norms of international law.
"We strongly recommend the leadership of the Democratic People's Republic of Korea think about whether a policy of opposing the entire international community meets the interests of the country," it said in a statement.
Nato Secretary General Jens Stoltenberg said the move was a "direct violation" of five UN resolutions and urged Pyongyang to "refrain from any further provocative actions".
One option on the table for the Security Council is whether to push for more tough sanctions.
But journalist Alex Jensen, in the South Korean capital Seoul, told Sky News North Korea was already one of the most sanctioned countries in the world.
He said: "At the UN Security Council, China - North Korea's ally - has veto-wielding power, but even if China were again to adopt sanctions on North Korea many observers say that officials in Beijing would turn a blind eye and let these sanctions be averted ... there is no sign Beijing would be willing to cut off Pyongyang."
Mr Kim has overseen two of the North's four nuclear tests and three long-range rocket tests since taking over after the death of his father, Kim Jong-Il, in late 2011.
Last month, the North claimed to have tested a hydrogen bomb - but this was widely disputed by experts.
Mr Kim has pledged to bolster its nuclear arsenal unless Washington scraps what Pyongyang calls a hostile policy meant to collapse his government.
Mr Jensen said: "It's pretty clear North Korea has a nuclear capability, it has nuclear weapons, but it's never been able to prove that it can mount nuclear material to a delivery system.
"By sending this rocket into space it's at least showing the US, in particular, that it has the ability to send a nuclear bomb to the American continent.
"Whether or not North Korea would use its nuclear weapons to attack another country remains to be seen, but it's a sort of a wink, wink - that we know that you know we have the ability to do this."
Source: http://news.sky.com/story/1637386/north-korea-we-will-launch-more-rockets