North Korea's claim to have successfully carried out a nuclear weapon test underground has sparked international condemnation.
South Korea said it had the capability to cope
President George W Bush said the US was working to confirm the claim, which he branded a "provocative" act.
He said he and regional leaders agreed North Korea's actions were unacceptable and deserved an immediate response from the United Nations Security Council.
Security Council members are meeting in New York to discuss their reaction.
South Korean media said the test took place in Gilju in Hamgyong province at 1036 (0136 GMT).
But both the US and Japan said they had detected seismic waves. Russia said it was "100% certain" a nuclear test had occurred.
The size of the bomb is uncertain. South Korean reports put it as low as 550 tons of destructive power but Russia said it was between five and 15 kilotons. The 1945 Hiroshima bomb was 12.5-15 kilotons.
BBC diplomatic correspondent Jonathan Marcus says North Korea's claimed test does not necessarily mean it has a fully-fledged nuclear bomb or warhead that it can deliver to a target.
In his first public statement, the US president said the North Korean claim "constitutes a threat to international peace and security."
He said he had telephoned Chinese, Japanese, Russian and South Korean leaders, who had all reaffirmed their commitment to a nuclear-free Korean peninsula.
"Once again, North Korea has defied the will of the international community, and the international community will respond," he said.
"The North Korea regime remains one of the world's leading proliferators of missile technology including transfers to Iran and Syria."
Mr Bush added that the development would not help North Korea's "oppressed and impoverished" people, who deserved a better future.
Japan's foreign ministry said Mr Bush and Japan's Prime Minister Shinzo Abe had agreed there should be "decisive UN action".
Mr Abe, currently visiting Seoul, earlier called the claimed test "unpardonable".
The region was "entering a new, dangerous nuclear age", Mr Abe said.
He said Japan and the US would step up co-operation on the missile defence system they began after a North Korean missile test in 1998.
South Korean President Roh Moo-hyun said it would be "difficult" to maintain his country's policy of engagement with the North. He feared the move could "spark a nuclear arms build-up in other countries".
The head of the South's intelligence service told lawmakers it had detected more movement at a North Korean test site and he could not rule out further nuclear tests.
In Seoul, about 500 protesters rallied against the claimed test, burning a portrait of North Korean leader Kim Jong-il.
South Korea has also suspended a scheduled aid shipment of concrete to North Korea.
In an unusually strong statement against its ally, China said the claimed test "defied the universal opposition of international society".
The BBC's Rupert Wingfield-Hayes in Beijing says China's statement is an indication of how strongly it is angered by North Korea's action, although Beijing will still be loath to support tougher sanctions against Pyongyang.
When it announced the test, the North's KCNA media agency described it as an "historic event that brought happiness to our military and people".
KOREAN NUCLEAR CRISIS
Sept 2005: At first hailed as a breakthrough, North Korea agrees to give up nuclear activities
Next day, N Korea says it will not scrap its activities unless it gets a civilian nuclear reactor
US imposes financial sanctions on N Korea businesses
July 2006: N Korea test-fires seven missiles
UN Security Council votes to impose sanctions over the tests
Oct 2006: N Korea claims to have carried out nuclear test
It said the test would maintain "peace and stability" in the region and was "a great leap forward in the building of a great prosperous, powerful socialist nation". There was no radiation leak, it said.
The development comes three days after the UN Security Council agreed on a formal statement urging North Korea to cancel any planned nuclear test and return to disarmament talks.
Pyongyang pulled out of the nuclear Non-Proliferation Treaty in 2003 and has refused for a year to attend talks aimed at ending its nuclear ambitions.
North Korea's official media has long warned that the US was preparing to attack and developing a nuclear capability was the only way to prevent this.
If confirmed, the test would make North Korea the ninth country known to have nuclear weapons.