Secretary of State Condoleezza Rice (search) said Monday the United States is stepping up cooperation to fight terrorism in Southeast Asia, warning that terror attacks remain a major threat across the region.

"The threat of extremism is a threat that is worldwide and has had its manifestation in Southeast Asia," she said, citing nightclub bombings in Bali, Indonesia, in 2002 that killed 202 people. "This is a region that does have a problem."

Southeast Asia terror leader Riduan Isamuddin, also known as Hambali (search), was arrested in Thailand in 2003 after an investigation assisted by Washington. He is now in U.S. custody.

Hambali is believed to be the main link between Al Qaeda and Jemaah Islamiyah (search), the regional terror group blamed for the Bali bombings, and a 2003 attack at the J.W. Marriott hotel in Jakarta, Indonesia that killed 12 people.

"With our regional partners, we're intensifying counterterrorism cooperation, we're intensifying intelligence cooperation, we're intensifying law enforcement cooperation," Rice said, without elaborating.

She added: "We've had training and tactical assistance on some of these matters with Thailand and we intend to continue that."

The further strengthening of the United States' relationship with Thailand in providing humanitarian assistance after the Dec. 26 tsunami has also helped bolster cooperation in dealing with terrorists, she said.

Rice arrived on the resort island of Phuket (search) late Sunday after talks in Beijing with Chinese leaders in a four-nation tour through Asia focused primarily on how to get North Korea to give up nuclear weapons development.

In a major breakthrough, Pyongyang said Saturday it would abandon a yearlong boycott and resume disarmament talks this month.

Rice spoke to reporters after meeting with Thailand's Prime Minister Thaksin Shinawatra (search) and Foreign Minister Kantathi Suphamongkhon (search) at the start of a one-day visit to review the country's efforts to rebuild coastal areas battered by the December tsunami.