Obama spoke with South Korean President Lee Myung-bak at midnight Sunday to discuss the situation, the White House said.
"We remain committed to stability on the Korean peninsula, and to the freedom and security of our allies," the White House said. The two leaders agreed to stay in close touch as the situation develops and to direct their national security teams to continue close coordination.
North Koreans were urged Monday to be loyal to Kim's son and apparent successor, Kim Jong Un.
The news of Kim's death during the weekend has left neighboring diplomats and political leaders anxiously awaiting some sign of North Korea's nuclear intentions, The New York Times reported.
China offered "deep condolences," calling Kim Jong Il a great leader of the North Korean people and a close friend to China, CNN reported.
Japan expressed hope Kim's death does not "have an adverse effect on peace and stability on the peninsula. South Korea urged residents to remain calm and continue their daily lives.
In Russia, Foreign Minister Sergei Lavrov said Moscow expects Kim Jong Il's death won't affect friendly ties between Russia and North Korea, Russia's Interfax news agency reported.
Australian Foreign Minister Kevin Rudd said Kim's death "presents an important opportunity to the new North Korean leadership to engage fully with the international community," CNN reported