"We expect the council to unanimously condemn what has happened and respond to this provocation and violation of international law," he had said before the meeting.
Calls for the meeting came after North Korea launched what is believed to be a three-stage Taepodong-2 missile, with an estimated range of 6,700km in violation of Security Council Resolution 1718.
Yukio Takasu, the Japanese ambassador the UN, said: "Thank God nothing fell on Japan. But it doesn't change the situation. It is a clear sign of intention and a threat to international peace and security."
At the request of the US and Japanese governments, the meeting was called by Claude Heller, Mexico's UN ambassador and chair of the 15-member council this month.
Resolution 1718, adopted in 2006 after North Korea's missile launch on July 5 and nuclear test on October 9 the same year, demands that the country refrain from any further nuclear testing or another ballistic missile launch.
Sunday's launch sparked alarm because North Korea has acknowledged it has nuclear weapons.
Barack Obama, the US president, called the rocket launch a "provocation" that required a strong international response by the security council, during a speech in Prague on Sunday.
"Rules must be binding, violations must be punished, words must mean something."
Al Jazeera's Kristen Saloomy, reporting from the UN, said the US, Japan, South Korea and EU countries were calling for a strong, unified condemnation from the UN Security Council.
But no one was sure if China or Russia, which hold veto power in the council, would support such a statement against North Korea, our correspondent said.
Yang Jiechi, the Chinese foreign minister, responded to the UN-member calls for condemnation on the ministry's website on Sunday: "Relevant parties must ... avoid taking actions that could make the situation even more tense."
Russia also urged restraint while a report said Moscow was studying whether Pyongyang had in fact broken any UN Security Council resolutions.
One diplomat, speaking on condition of anonymity, said the council might end up with a resolution or a non-binding statement that would reaffirm existing sanctions.
For several tense minutes on Sunday, North Korea's rocket flew through Japan's airspace, which had given its military the authority to shoot down any threat - something Pyongyang had warned would be seen as an act of war.
North Korean state media reported that Pyongyang had sent a satellite into space at 00:29GMT on Sunday and that it was now circling the earth.
But Japan said the booster rockets fell harmlessly into the water, while the United States and Seoul said the launch had failed to get its payload, a satellite, into orbit.
South Korea called the launch "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 spokesman for South Korea's president, said.
"The government will deal firmly and resolutely with North Korea's provocative act."