The UN Security Council is to hold an emergency session on the development later in the day.
The rocket passed over Japan on its way towards the Pacific Ocean.
Pyongyang previously said that it would send a communications satellite into orbit as part of a peaceful space programme.
South Korea, Japan and the US allege that North Korea is using the launch to test its Taepodong-2 long-range missile, which is capable of reaching the US.
The launch has sparked alarm because North Korea has acknowledged it has nuclear weapons.
Barack Obama, the US president, said the launch further isolated North Korea and that the country must abandon its pursuit of weapons of mass destruction to find acceptance in the international community.
Ban Ki-moon, the UN secretary-general, and the European Union separately said that the firing of the rocket threatened regional stability.
China, which has close ties to Pyongyang, called on all sides to maintain calm and restraint, and Russia also called for restraint.
Fred Lash, a US state department spokesman, told reporters: "We have had a launch. I don't know the type of missile."
Lash called the move a "provocative act" and said the US would "take appropriate steps to let North Korea know that it can't threaten the safety and security of other countries with impunity and acts like these".
"North's Korea's development, deployment and proliferation of missiles, ballistic missile-related materials, equipment and technologies pose a serious threat to the northeast Asia region and to the international community," he said.
South Korea said that the launch was "reckless".
"The government cannot but express disappointment and regret over North Korea's reckless act of firing a long-range rocket, which poses a serious threat to security on the Korean peninsula and the world," Lee Dong-Kwan, a South Korean presidential spokesman, said.
"The government will deal firmly and resolutely with North Korea's provocative act," Lee said without giving further details.
"It is extremely regrettable that North Korea went ahead with the launch ... and we protest strongly," Takeo Kawamura, Japan's chief cabinet secretary, said.
"It has flown over Japan so no orders have been issued to intercept or destroy the projectile," he said.
Tensions over the launch have run high. On Saturday, the Japanese government, reported that North Korea had launched the rocket but later retracted the news, blaming a faulty detection device for the erroneous information.
Wayne Hay, Al Jazeera's correspondent in Paju on the South Korean side of the border with the North, said that although it was a satellite launch, South Korea remained cautious.
"I don't think that in this particular launch they would be worried. But [South Korea] have stuck to the line that this is a cover for a ballistic missile test," he said.
Our correspondent said that South Korea has ordered 655,000 troops to be on high alert to guard against any provocative activity.
Leonid Petrov, a research associate at the School of Pacific and Asian Studies at the Australian National University, said that the launch had been successful.
"It looks like everything is under control and there was a significant development and improvement into the technology... because previous launches either failed or there was a controlled explosion 42 seconds after launch," he said.
Petrov said the launch sent two strong messages: "One to enemies ... that North Korea has a new technology for deterrence. So nobody should interfere into North Korean domestic affairs, otherwise there will be retaliation.
"[And one] to friends ... that North Korea is possessing a superior technology not only in satellite launching but also as a duel technology in missile launching," Petrov said.
Donald Kirk, a correspondent for the Christian Science Monitor and North Korea specialist, told Al Jazeera that the launch may add complications for the six party talks - meetings that have been taking place between North and South Korea, Russia, China, Japan and the US to find a peaceful resolution to Pyongyang's nuclear programme.
"It could make things considerably more difficult ... South Korea could intensify cooperation with PSI, the Proliferation Security Initiative," Kirk said.
"On the other hand ... maybe the US will press harder for dialogue ... [and they] will be able to get together on two-sided talks as a prelude to six party talks and the process could speed up."
Pyongyang fired a Taepodong-2 missile in a July 2006 test session but it exploded shortly after launch. It conducted a nuclear weapons test, its only one to date, in October 2006.