Mr. Bush's comments come after North Korea earlier Wednesday warned South Korea that it will take "corresponding" action if the South takes part in international sanctions against the North over its nuclear test earlier this month.
The president told reporters Wednesday that the United States, South Korea, China, Russia and Japan all agree they need to work together to solve the issue peacefully.
Secretary of State Condoleezza Rice said in a speech earlier in the day that she was pleased by the serious commitment of U.S. friends and allies to the Security Council resolution.
It prevents trade in a range of goods, freezes North Korean assets, and bans travel for people connected to North Korea's nuclear weapons program.
South Korea has indicated it has formed a task force to study how to impose the sanctions.
Meanwhile, Russian President Vladimir Putin is urging the international community to adopt a more constructive approach to resolving the North Korean nuclear crisis, saying that pressuring the reclusive state is counterproductive.
Mr. Putin said Wednesday that one of the reasons Pyongyang conducted a nuclear test October ninth was because some participants of the six-nation disarmament talks could not find the "right tone" in the negotiations.
On Tuesday, China said North Korean leader Kim Jong Il had told Beijing officials he is not planning to conduct another nuclear test, unless international pressure provokes Pyongyang to change its course.
North Korea says it will return to the six-nation talks only if Washington lifts sanctions, including a freeze on the North's funds held in a bank in Macau. U.S. authorities say the sanctions are a separate issue from the talks.
They say they froze the funds because North Korea produces and circulates counterfeit U.S. currency, and is engaged in money-laundering activities.
Information for this report is provided by EAP, mkm, caw