Late on Monday the UN Security Council strongly condemned Pyongyang. Diplomats have begun drafting a resolution to punish the communist state.
But North Korea appeared unbowed; South Korea said its northern neighbour could be preparing more missile tests.
North Korea announced it had carried out a nuclear test early on Monday.
In a strongly-worded statement carried by the state news agency on Tuesday, it said it was prepared to fight.
"It is clear that nothing has changed in the US hostile policy against DPRK [North Korea]... even under the new US administration," it said in an article criticising recent US moves to relocate its fighter jets.
See map of test site
"Our army and people are fully ready for battle... against any reckless US attempt for a pre-emptive attack," it said.
Coordinated defence
Mr Obama spoke by phone late on Monday with his South Korean counterpart Lee Myung-bak and Japanese Prime Minister Taro Aso to "coordinate" reaction to North Korea's nuclear test.
The White House said they agreed to work towards "a strong United Nations Security Council resolution with concrete measures to curtail North Korea's nuclear and missile activities".
In his talks with Mr Aso, Mr Obama reiterated his country's "unequivocal commitment to the defence of Japan and to maintaining peace and security in Northeast Asia".
South Korean and Chinese defence ministers are set to discuss joint action, South Korean media reported.
The discussions followed an emergency meeting of the UN Security Council in New York, where members voiced strong opposition to the test and condemned it.
The US ambassador to the UN, Susan Rice, said America wanted "strong measures" when it starts work on the resolution.
"The US thinks that this is a grave violation of international law and a threat to regional and international peace and security," she said.
Russia's UN envoy told reporters the nuclear test was a clear violation of UN Resolution 1718. That resolution imposed sanctions on North Korea after its first test.
The UK's Ambassador to the UN, Sir John Sawers, explained that the Council had decided to act in two stages, first issuing a statement "strongly condemning and opposing what the North Koreans have done by carrying out this second nuclear test".
"And we decided to start work immediately on a further Security Council resolution in order to uphold the international peace and security in the region," he added.
More missile tests?
But there was no sign that the criticism would influence North Korea.
South Korean military sources have warned of signs that the North may be preparing to fire anti-ship missiles off its west coast. A number of missile tests accompanied Monday's nuclear test.
The government in Seoul has announced it will delay no longer in joining the PSI - a US-led non-proliferation campaign aimed at stopping the trafficking of weapons of mass destruction.
North Korea has repeatedly warned that the South's participation in the PSI would be tantamount to a declaration of war.
The heightened fears of conflict follow weeks of warnings from North Korea that it would strengthen its "deterrent", and came after the communist state walked away from long-running negotiations on its nuclear programme amid deadlock with the US.
The international community faces a difficult task, confronting what many view as a dangerously unpredictable regime, BBC world affairs correspondent David Loyn reports.
Monday's blast, which was estimated by international seismologists to have the power of a 4.5 magnitude earthquake, appears to have been much more powerful than North Korea's first nuclear test, in October 2006.
Defence officials in neighbouring Russia say it was an explosion of up to 20 kilotons, making it comparable to the American bombs that flattened Hiroshima and Nagasaki in 1945.
