Pyongyang insists its space programme is purely scientific, but most of the world views its rocket launches as disguised ballistic missile tests aimed at developing a weapons delivery system capable of striking the US mainland.
There was no immediate confirmation that the final stage of the satellite-bearing rocket had successfully achieved orbit, and an unconfirmed report from South Korea's Yonhap news agency suggested the second stage may have malfunctioned.
A US defence official said the launch vehicle "appears to have reached space."
Condemnation was swift, with the United States calling the launch "destabilising" and provocative, while Japanese Prime Minister Shinzo Abe slammed it as "absolutely intolerable."
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In New York, diplomats said the UN Security Council would meet in emergency session later today.
South Korean President Park Geun-Hye said the Council should respond quickly with "strong punitive measures" against what she called a grave challenge to global peace and security.
The rocket, carrying an Earth observation satellite, took off at around 9:00 am Pyongyang time, according to the South Korean defence ministry which was monitoring the launch site.
Multiple UN Security Council resolutions proscribe North Korea's development of its ballistic missile programme.
Despite Pyongyang's insistence on a peaceful space mission, its rockets are considered dual-use technology with both civil and military applications.
The United States, along with allies like South Korea and Japan, had warned Pyongyang it would pay a heavy price for pushing ahead with launch, but analysts said the North's timing was carefully calculated to minimise the repercussions.
"North Korea likely calculates that a launch so soon after the nuclear test will probably only incrementally affect the UN sanctions arising from that test," said Alison Evans a senior analyst at IHS Jane's.
North Korea's chief diplomatic ally, China, has been resisting the US push for tougher sanctions against Pyongyang.