The blast, which tore through a bustling market in the heart of Davao city on Friday, killed at least 14 people and led to the president imposing a "state of lawlessness" in the country.
The head of Davao police today described how a man was seen leaving a bag with the bomb inside at the market while being followed by two women.
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.
"We believe the improvised explosive device exploded when the person left," he said, adding that the two women had been following the man.
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Another person may have detonated the device with a cellphone, he suggested.
He would not say who was behind the blast but said the bomb, using a mortar shell, was similar to those used by "threat groups" in the troubled central region of Mindanao.
There are several Muslim outlaw groups in that area, including separatist guerrillas but the Abu Sayyaf are based elsewhere, in the southern islands of Jolo and Basilan.
He has said that the explosion was in retaliation for the military operation against the group in their stronghold in Jolo.
However Chief Inspector Andrea De la Cerna, spokeswoman of a task force investigating the explosion, said they were not ruling out other motives for the attack.
"We have copies of the CCTV (closed-circuit television), we have eight possible witnesses but we have named no one (as suspects)," she told AFP.
Duterte believes the attack was "80 percent" likely an act of terrorism, his spokesman, Martin Andanar told reporters today.
The military is continuing to press an offensive against the Abu Sayyaf in Jolo following a clash on August 29 that left 15 soldiers dead.