Duterte, who was in Davao at the time of the attack but not near the market, told reporters before dawn Saturday that it was an act of terrorism, as he announced extra powers for the military.
“These are extraordinary times, and I’m authorized to allow the security forces of this country to do searches”, Duterte told reporters.
He clarified that it is not a declaration of martial law. Duterte’s office has said that his proclamation was based on an article in the country’s Constitution that puts its leader in charge of armed forces.
Duterte had been at a meeting some 12 km (7.5 miles) away from downtown Davao when the explosion occurred.
Police are searching for the three – and possibly a fourth person – over the bombing, which has been widely blamed on the Muslim extremist Abu Sayyaf group.
The Foreign Ministry said Singapore condemned the explosion, which “killed and injured many innocent people”.
Police refused to elaborate except to say they wanted to question the suspects for their possible involvement in Davao City, the hometown of Duterte and Director General Ronald dela Rosa, the head of the Philippine National Police.
Police and the military promised to implement the nationwide “state of lawlessness”, although there appeared to be confusion about what that actually entailed.
“It remains to be seen whether the declaration of lawlessness will see the imposition of hardline security policies by Duterte against Islamic militants in a manner similar to the bloody war on drugs or whether the Filipino president can clamp down on the ‘environment of lawless violence” without a major increase in bloodshed.
Dozens more were wounded in the explosion at a packed market in the southern city of Davao.
Rumours have swirled in recent days of a plot to assassinate Duterte, 71, which he has shrugged off as part of his job.
Mr Duterte was elected President in June, launching a campaign he claimed would kill so many drug users and dealers that “fish will grow fat” from bodies dumped in Manila bay. His spokesman, Ernesto Abella, urged the public to be vigilant. He typically spends his weekends in Davao. “At least we know who made the threats”.
Philippine media has reported that the terror group Abu Sayyaf on Saturday claimed responsibility for the explosion, the deadliest attack in the city since 2003, when twin bombings struck the Davao International Airport, killing 22, and the Sasa Wharf, where 17 perished. The attack comes on the heels of Duterte beginning an overseas trip to Brunei, which he then cancelled.
The region is also home to Abu Sayyaf, a rebel group loosely linked to Islamic State of Iraq and the Levant (ISIL, also known as ISIS) and notorious for making tens of millions of dollars from kidnappings.
They are being hit by stepped-up offensives after Duterte ordered the military to wipe the group out.
The group’s spokesperson Abu Rami said the attack was a “call for unity to all mujahideen in the country” in response to the government’s military operations against them.