Among those to condemn the move was its only major ally, China, which summoned the North Korean ambassador.
The reclusive North said the test was an act of self-defence against US hostility and threatened stronger steps if necessary.
It said the test had greater explosive force than the 2006 and 2009 tests.
The country said it had used a miniaturised and lighter nuclear device, indicating it had again used plutonium, which is more suitable for use as a missile warhead.
North Korean leader Kim Jong-un, the third of his line to rule the country, has presided over two long-range rocket launches and a nuclear test during his first year in power, pursuing policies that have propelled his country closer to becoming a nuclear power.
China summoned the North Korean ambassador in Beijing and protested sternly. Foreign Minister Yang Jiechi said China was unhappy and opposed to the test. He urged North Korea to "stop any rhetoric or acts that could worsen situations".
US President Barack Obama called the test a highly provocative act that hurt regional stability and pressed for new sanctions.
He said: "The danger posed by North Korea's threatening activities warrants further swift and credible action by the international community.
"The US will also continue to take steps necessary to defend ourselves and our allies."
UK Foreign Secretary William Hague called the test a violation of UN Security Council resolutions. He said: "North Korea's development of its nuclear and ballistic missile capabilities poses a threat to international and regional security.
"Its repeated provocations only serve to increase regional tension, and hinder the prospects for peace on the Korean Peninsula."
Russian Foreign Minister Sergei Lavrov urged North Korea to abandon its nuclear arms programme and return to talks.
UN Secretary-General Ban Ki-moon and Nato also condemned the move.
However, a spokesman for the North Korean Foreign Ministry said the test "was only the first response we took with maximum restraint".
He added: "If the United States continues to come out with hostility and complicates the situation, we will be forced to take stronger, second and third responses in consecutive steps."
North Korea often threatens the US and South Korea with destruction in colourful terms.
The magnitude was twice as large as 2009, Lassina Zerbo, director of the international data centre division of the Vienna-based Comprehensive Nuclear-Test Ban Treaty Organisation, said.
Despite China's strong response, the test is likely to be a major embarrassment for Beijing, the North's sole major economic and diplomatic ally.
Mark Fitzpatrick, of the International Institute for Strategic Studies think tank, said: "The test is hugely insulting to China, which now can be expected to follow through with threats to impose sanctions."
North Korea trumpeted the announcement on its state television channel.
It linked the test to its prowess in launching a long-range rocket in December, a move that triggered UN sanctions Pyongyang said prompted it to take the action.