Bush's response follows China's condemnation of North Korea's nuclear test, which described it as "brazen".
Bush declined to confirm Pyongyang's claim to have carried out such a test but said that he had spoken to the leaders of China, South Korea, Russia and Japan about the response.
"All of us agreed that the proclaimed actions taken by North Korea are unacceptable and deserve an immediate response by the United Nations Security Council," said the US president.
"Such a claim itself constitutes a threat to international peace and security. The United States condemns this provocative act."
John Bolton, the US ambassador to the UN, was drawing up a Security Council draft resolution, which includes 13 elements that members are considering. But it is not clear whether Russia and China will impose sanctions, although they condemned the testing.
Among the US proposals are an arms embargo, the freezing of financial assets connected with weapons of mass destruction and a ban on luxury items, according to a document read to Reuters.
The UN Security Council also condemned North Korea's first nuclear weapons test, saying it was in defiance of a UN resolution.
Japan's UN envoy Kenzo Oshima, the current council president, read out a statement urging North Korea "to refrain from further testing" and return to six-nation disarmament talks.
North Korea pulled out of the talks with South Korea, China, the US, Japan and Russia in November.
Kofi Annan, the UN secretary-general, expressed deep concern, saying the test would aggravate tensions on the divided Korean peninsula.
Japanese prime minister Abe said
the test was unpardonable
Ban Ki-Moon, the next UN secretary-general and South Korea's foreign minister, reacted with similar alarm, describing the test as a "grave and direct threat to peace and stability on the Korean peninsula and in Northeast Asia".
He added that the Seoul government "will be firm and resolute in adhering to the principle of no tolerance for a nuclear North Korea".
China's foreign ministry said in a statement: "On October 9, the DPRK (North Korea), ignoring the general opposition of the international community, brazenly undertook a nuclear test. The Chinese government expresses its resolute opposition.
"China strongly demands the DPRK side to undertake its commitments to the non-nuclearisation of the Korean Peninsula, and stop all actions that can lead to the deterioration of the situation."
China called on North Korea to return to the six-party talks on Pyongyang's nuclear programme that were abandoned last year.
China also urged nations to react peacefully to the nuclear test.
"The Chinese government calls on all sides to deal with this calmly and seek consultations to peacefully resolve the issue."
For his part, Shinzo Abe, the Japanese prime minister, said North Korea's test was unpardonable.
Abe, who arrived in Seoul on Monday from Beijing for a summit with Roh Moo-Hyun, the South Korean president, made the remarks during a lunch with Han Myeong-Sook, the country's prime minister.
Abe said: "North Korea's nuclear weapons test can never be pardonable. But we should collect and analyse more intelligence on the matter in a cool-headed manner.
"Whatever provocation by North Korea should be dealt with with a cool head. Maintenance of bilateral relations [between Japan and South Korea] is important."
Russia said it had detected an explosion of between five and 15 kilotonnes - more powerful than the US atomic bomb that destroyed Hiroshima in 1945.
Vladimir Putin, the president, said Russia "unconditionally condemned" the test. He added it had caused "huge damage" to the nuclear non-proliferation process.
A protester at an anti-North
Korea meeting before the test
Iran also commented on the test as world powers are due to discuss sanctions against Iran over its own nuclear programme.
Mohammad Ali Hosseini, a foreign ministry spokesman, said: "Iran's position is clear and Iran on principle believes in a world free of nuclear weapons.
"Iran is hopeful that negotiations on North Korea's nuclear activities can go ahead in the interest of both North Korea and the international community," he added.
Iran has always denied US allegations that it is seeking nuclear weapons, saying the pursuit of such arms goes against Islam.
It insists its nuclear programme is for energy generation.
Mohamed ElBaradei, the head of the UN International Atomic Energy Agency in Vienna, said the test, if confirmed, would represent a grave threat to world security.
It "creates serious security challenges not only for the East Asian region but also for the international community", he said, calling for a legally binding universal ban on nuclear testing.