Australia said it feared more attacks and joined Britain and the United States in urging their citizens to stay indoors.
Involvement of Muslim militants, whose insurgency has cost more than 1,800 lives over the past three years but has remained confined to the far south, was a "very remote possibility", Surayud said.
Coup leader General Sonthi Boonyaratglin, Thailand's first Muslim army chief who cut short his Haj and returned to Bangkok on Monday, ruled out any links to foreign terrorist groups such as al Qaeda.
Security analyst Panitan Wattanayagorn said the bombings appeared to be locally planned and politically motivated, perhaps by those facing corruption probes by the post-coup government.
"Their aim may be to destabilize the government to make sure the accusations against them are dropped or negotiated," the Chulalongkorn University lecturer told Reuters.