President Bush has condemned North Korea's nuclear test claim, calling it a provocative act. Mr. Bush is calling for an immediate response by the United Nations.
President Bush says North Korea's claim constitutes a threat to international peace and security.
He said, "The United States condemns this provocative act. Once again, North Korea has defied the will of the international community, and the international community will respond."
In a brief statement from the White House, Mr. Bush said he has already discussed the matter with the leaders of Russia, China, South Korea and Japan - America's partners in multilateral negotiations with Pyongyang.
"We reaffirmed our commitment to a nuclear-free Korean Peninsula, and 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," he said.
The president did not indicate the United States has been able to verify North Korea's claim that it conducted a test Monday morning, local time. But he left no doubt, there is mounting concern, and a growing international will to increase pressure on Pyongyang.
He said North Korea is one of the world's leading proliferators of missile technology, including transfers to Iran and Syria.
Mr. Bush spoke of the possibility North Korea could now share its nuclear technology with others, calling it a "grave threat" to the United States. He said, if that happens, North Korea will be held fully accountable.
President Bush stressed the United States wants to resolve the matter through diplomacy. But he said he has assured U.S. allies in the region that America will live up to its security commitments. And he issued a warning to Pyongyang.
He said, "Threats will not lead to a brighter future for the North Korean people, nor weaken the resolve of the United States and its allies to achieve the de-nuclearization of the Korean Peninsula."
The United States has rebuffed North Korean calls for bilateral negotiations, saying the only way to deal with Pyongyang's nuclear ambitions is through multilateral diplomacy.
The six-party talks with North Korea have yielded little if any progress on the matter, though there have been signs of heightened pressure on Pyongyang from Beijing and Seoul.
The United Nations appears to be the current venue for diplomatic action, with indications following the North Korean test claims that there is growing sentiment among Security Council members for sanctions.