Facing the first direct challenge to his administration by an emerging nuclear weapons state, President Obama declared Monday that the United States and its allies would “stand up” to North Korea, hours after that country defied international sanctions and conducted what appeared to be its second nuclear test.

Mr. Obama reacted to the underground blast as White House officials scrambled to coordinate an international response to a North Korean nuclear capacity that none of his predecessors had proved able to reverse.

Acutely aware that their response to the explosion in the mountains of Kilju, not far from the Chinese border, would be seen as an early test of a new administration, Mr. Obama’s aides said they were determined to organize a significantly stronger response than the Bush administration had managed after the North’s first nuclear test, in October 2006.

Speaking in the Rose Garden after returning to the White House from Camp David and meeting with his top aides in the Oval Office, Mr. Obama vowed to “take action” in response to what he called “a blatant violation of international law” and the North’s declaration that it was repudiating past commitments to dismantle its nuclear program.

But as they had meetings every few hours — including a lengthy session in the Situation Room on Monday evening — some of Mr. Obama’s aides acknowledged that the administration’s options were limited.

Much depends, they said, on the new president’s ability to persuade Russia and China to go significantly beyond the strong condemnations that they issued Monday against North Korea, their former ally and a vestige of cold-war communism.

“I think we were all impressed with the fact that the Russians and the Chinese denounced this so strongly,” Rahm Emanuel, Mr. Obama’s chief of staff, said in a telephone call.

Yet turning that into effective action will prove a challenge.

Efforts by the Clinton administration to entice the North to halt its weapons program by providing it with oil and nuclear power plants, and by the Bush administration to push the country to collapse and then to try to seize its leaders’ assets, all failed. ....