President Bush has warned that North Korea would face a "grave consequence" if it transferred nuclear weapons to Iran or al-Qaida.
Mr. Bush told the ABC television network Wednesday that North Korea would be "held to account" if such a transfer took place.
He did not elaborate, but said the United States would use "means necessary" to hold North Korea to account.
U.S. Secretary of State Condoleezza Rice is in Asia for meetings on North Korea's recent nuclear weapon test and the subsequent U.N. Security Council sanctions.
She meets in Tokyo on Thursday with Japan's Prime Minister Shinzo Abe, then heads to Seoul.
Wednesday in Tokyo, Rice and Japanese Foreign Minister Taro Aso pledged to work together to implement the sanctions in response to Pyongyang's weapon test last week.
Rice also reaffirmed what she called Washington's firm commitment to the defense of Japan in accordance with security arrangements and commitments.
South Korea's government has welcomed the sanctions, which forbid trading activity that might help the North Korean nuclear program.
North Korea has said it considers the sanctions a declaration of war.
U.S. officials say American spy satellites have detected vehicle movements in North Korea that may signal preparations for another nuclear test.
Rice is to also visit Beijing and Moscow.