Speaking at a White House press conference on Wednesday, George Bush said that North Korea's claim it had successfully tested a nuclear bomb constituted "a threat to international peace and stability".
He also said that the US would would boost military co-operation with allies in the Asia Pacific region, including bolstering ballistic missile defenses there and increasing efforts to prevent the Pyongyang regime from importing missile and nuclear technology.
"The United States also reserves all options to defend our friends and our interests in the region against the threats from North Korea," he said.
North Korea, one of the world's most secretive and isolated nations, said the test was carried out on Monday at an underground site in the country's north east.
The announcement sparked international condemnation.
The US president ruled out bilaterial talks with North Korea and Iran, also at odds with the US administration over its nuclear programme, saying it was better to deal with the crises through multilateral talks.
"The US message to North Korea and Iran and the people in both countries is that we want to solve issues peacefully"
George Bush, US president
"I firmly believe that, with North Korea and with Iran, that it is best to deal with these regimes with more than one voice," Bush said.
"But the US message to North Korea and Iran and the people in both countries is that we want to solve issues peacefully."
Bush also said he supported the resumption of six-way talks among North Korea, South Korea, China, Russia, Japan and the US, which have been suspended for more than a year.
The US president also called on the United Nations security council to create a resolution that would specify measures to prevent North Korea from exporting nuclear or missile technologies and prevent financial transactions that would help it develop nuclear missile capabilities.
'Declaration of war'
North Korea said in a statement on Wednesday that it was ready for both "dialogue and confrontation".
"If the US continues to harass and put pressure on us, we will regard this as a declaration of war and will take a series of physical countermeasures," said a foreign ministry statement carried by the North's official Korean Central News Agency.
North Korea's number two leader had earlier warned Pyongyang may carry out more nuclear tests if the US continues its "hostile attitude" towards the communist state.
Kim Yong Nam, president of the Presidium of the Supreme People's Assembly, said in an interview with Japan's Kyodo news agency that the issue of future nuclear tests "is linked to US policy toward our country".
Japan said on Wednesday that it was to impose new sanctions on North Korea in addition to those imposed after Pyongyang test-fired missiles in July, included barring all North Korean ships from Japanese ports and banning imports.