Obama called the test "a blunt violation of international law" and said Pyongyang had reneged on its commitment to abandon its nuclear ambitions.
He was later reported to have phoned the leaders of Japan and South Korea to assure them of America's "unequivocal commitment" to their defence.
In a further escalation of tensions on Tuesday, South Korea's defence ministry said it had intelligence North Korea was preparing to test fire short-range missiles off its coast.
Any test launch would be the fourth fired by North Korea this week.
The missiles, based on China's Silkworm weapons system, are believed to have a range of about 160km.
'Price to pay'
The UN talks were preceded by a "P5 + 2" session between the five permanent members of the Security Council - Britain, China, France, Russia and the US - plus Japan and South Korea.
Ban Ki-Moon, the UN secretary general, also joined widespread international criticism of the test, saying he was "deeply disturbed" by reports it had taken place.
"They should have come to the dialogue table and resolved all the issues through peaceful means," he said.
Following the UN talks several diplomats hinted that they would push for fresh sanctions against North Korea under a new resolution.
"This resolution should include new sanctions in addition to those already adopted because such behaviour should have a cost and a price to pay," Jean-Pierre Lacroix, the French Deputy Permanent Representative told reporters.
Susan Rice, the US ambassador to the UN, said Washington would seek "a strong resolution", calling the test "a grave violation of international law, and a threat to regional and international peace and security."
Rice however stopped short of mentioning possible sanctions.
John Bolton, a former US ambassador to the UN during the Bush administration, told Al Jazeera the US needed respond to the test using "strong measures".
"I think we should conclude from this that North Korea is not going to be talked out of its nuclear programme".
"I would recommend economic sanctions along the lines of those imposed on Iraq after the invasion of Kuwait in 1990...I believe this is a case that calls for North Korea to be expelled from the United Nations for persistent violations of its charter".
Bolton also said the US should "return North Korea to the list of state sponsors of terrorism".
|The test site is believed to be near the northeastern town of Kilchu
China, Japan, Russia, South Korea and the US have been negotiating since 2003 to persuade the North to abandon its nuclear weapons work in exchange for energy and security guarantees.
The six-party talks led to a 2007 agreement under which the North said it would dismantle its nuclear facilities, but the deal stalled during disagreements over verification.
In April, North Korea fired a three-stage rocket that it said launched a satellite into orbit, although the the US has said it believes the launch was a cover for a test of the North's long-range missile technology.
The launch triggered condemnation from the Security Council, in turn provoking an angry reaction from the North, which said it was pulling out of nuclear disarmament talks and restarting its weapons programme.
The exact size of North Korea's latest test has not been confirmed, although state media in its official announcement of the test said it had been on "a higher level in terms of its explosive power" than previous detonation in 2006.
Russia's defence ministry said an atomic explosion at had taken place in northeastern North Korea, 0954am (0054GMT) and estimated the blast's yield to be up to 20 kilotonnes, about the same as the US bombs used against the Japanese cities of Nagasaki and Hiroshima at the end of World War Two.
The US Geological Survey (USGS) earlier said it had detected a magnitude 4.7 tremor near the town of Kilchu about 375km northeast of Pyongyang, the capital, and close to where North Korea conducted its first nuclear test in October 2006, which was estimated to be about one kilotonne.