Hambali is at the top of Indonesia's wish list. The 39-year-old Indonesian is alleged to have been behind a series of terror attacks in Indonesia and across Southeast Asia, including last year's devastating Bali bombing, which killed 202 people.

The Afghanistan-trained Hambali is alleged to have been one of the most senior members of regional terror group Jemaah Islamiyah, and the group's main link to Osama bin Laden's al-Qaida network.

President Bush declined to say when Hambali might be handed over, but observers say that the United States is more interested in extracting information from him than insisting that he be tried on U.S. soil.

The promise to give back Hambali caps what many people believe was a successful, if brief, visit by Mr. Bush to Indonesia Wednesday.

Hambali (Police handout)

During a 3 1/2-hour stop on the resort island of Bali, Mr. Bush praised President Megawati Sukarnoputri, calling her an ally against terrorism. And, at a meeting with moderate religious leaders, he tried to dispel the conviction of many Muslims that the war on terror is a war against Islam.

He also offered substantial financial assistance for the country's fledgling democracy and to train Indonesia's security forces.

But hostility to U.S. policy in the Middle East and Iraq runs deep in Indonesia, the world's largest Muslim nation. Many people feel that the battle lines in the war on terror have been unacceptably widened.

Landry Subianto is with The Centre for Strategic and International Studies in Jakarta.

"I think what has been perceived in Indonesia is that the anti-terrorist campaign in terms of war is mostly targeted at the country which happen to be populated mostly by the Muslims," said Landry Subianto.

President Bush's comments on Thursday that he sees Australia as a regional guarantor of security in Southeast Asia have proven particularly controversial in Indonesia, Australia's northern neighbor.