The rocket blasted off from the Musudan-ri launch site in the north-east of the country at 0230 GMT.
North Korea said it was sending a satellite into orbit, but its neighbours suspect the launch was a cover for a long-range missile test.
They strongly
condemned1 the launch. The US president told Pyongyang to "refrain from further
provocative2 actions".
North Korea had "ignored its international obligations, rejected unequivocal calls for restraint, and further
isolated3 itself from the community of nations", Barack Obama said in a written statement.
Japan called the move "extremely regrettable", while South Korea said it constituted a clear
breach4 of a
United Nations resolution.
UN Secretary General Ban Ki-moon said North Korea's actions were not
conducive5 to regional stability, as did the European Union. China and Russia both called on all sides to act with restraint.
The UN Security Council has approved a Japanese request for an emergency session later in the
day in New York.
No intercept6 North Korea announced several weeks ago that it planned to send what it called an "experimental communications satellite" into space.
Its rocket blasted off just before midday local time, within a pre-announced launch window.
It flew over Japan towards the Pacific, with two booster stages dropping into the ocean to the east and west of Japan, Tokyo said.
Japan said it had not tried to intercept the rocket. It had indicated it would do so if the rocket threatened its territory.
North Korea says that the launch is part of what it calls peaceful space development.
An unidentified South Korean official told Yonhap news agency that the rocket did appear to be carrying a satellite. It is not clear whether a satellite was successfully put into space.
If it is confirmed, North Korea will see this as a major propaganda victory, says the BBC's John Sudworth in Seoul.
But of more concern to Pyongyang's neighbours is the potential military use of the launch vehicle, our correspondent says.
They believe the real aim of the launch was to test long-range missile technology; specifically the Taepodong-2.
They believe it could put parts of the US within the communist nation's military reach.
North Korea first tested a Taepodong-2 in July 2006. It failed less than a minute after lift-off.
Three months later, Pyongyang carried out a nuclear test. International talks involving the US, South Korea, Japan, Russia and China on an aid-for-nuclear disarmament deal are currently stalled.