The fiery leader, who has threatened to eat the militants alive in a bloodthirsty vow of revenge for the attack in Davao that killed 15 people, said the group was no longer just after money from criminal activities.
Several units of the Abu Sayyaf in the strife-torn southern Philippines have pledged allegiance to the Islamic State group but analysts have said they are more interested in funding than ideology.
"They are hungry for a fight to establish a caliphate in Southeast Asia. Caliphate is a kingdom for the Muslims," Duterte said in a speech to soldiers.
"The problem is that they do not talk on the basis of what school you can give them," he said referring to previous local services the militants have asked for.
"It's either the caliphate or nothing."
The Abu Sayyaf is a radical offshoot of a Muslim separatist insurgency in the south of the mainly Catholic Philippines that has claimed more than 120,000 lives since the 1970s.
The Philippine defence department has said there were no formal links between the group and the Islamic State which holds vast swathes of Iraq and Syria.
"They are ISIS inspired and not actually ISIS supported. They are just ISIS wannabes," defence department spokesman Arsenio Andolong told AFP, using another name for the Islamic State.
Duterte, who has restarted peace talks with the country's two major Muslim rebel groups since taking office on June 30, initially pleaded for peace with Abu Sayyaf but has since hardened his position and branded them as terrorists.
Last month, he launched an offensive against the militants, ordering the military to "destroy" them.
He sent thousands of troops to Abu Sayyaf strongholds in the southern islands of Jolo and Basilan in an assault that had killed 15 soldiers and 32 militants according to the military.
The Abu Sayyaf is blamed for the nation's worst terror attacks and has beheaded foreigners, including two Canadians in April and June after ransom deadlines lapsed.
The militants have also conducted high seas kidnappings in waters bordering the Philippines, Indonesia and Malaysia, prompting the three nations to launch joint patrols.