Hambali, said to be Osama bin Laden's point man in the region, is also wanted in Malaysia, Singapore and the Philippines.
Hambali is believed to have entered the country with a fake Spanish passport from neighboring Laos through a land border crossing, local newspapers reported.
Thaksin said he has instructed immigration officials at border crossings to be more vigilant in checking for fake passports.
The Nation reported on Friday that Hambali was plotting a terrorist attack for a forthcoming summit in Bangkok of Asia Pacific leaders, including US President George W. Bush. But this remains unconfirmed.
Indonesia has said it will seek Hambali's extradition for trial in Bali.
Malaysia also said Friday it wants to interrogate Hambali, who is believed to have hosted a meeting of senior al-Qaeda operatives, including two Sept. 11 hijackers, in Kuala Lumpur in January 2000.
A top al-Qaeda detainee has told US interrogators of Hambali's assignment to find more suicide hijackers not long after the Sept. 11 attacks, a senior Bush administration official said.
Thai authorities are believed to have known Hambali was in the kingdom in January last year.
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