"I can eat you," Duterte said, talking tough about terrorists. "Just give me salt and vinegar. True. Make me mad. Get me a terrorist.
"Give me salt and vinegar. I will eat his liver."
Lecter is the fictional killer cannibal of "The Silence of the Lambs," known for famously hissing, "A census taker once tried to test me. I ate his liver with some fava beans and a nice Chianti."
Duterte's eye-popping comments came after members of the jihadist militant group Abu Sayyaf Group (ASG) clashed with Philippines government troops on the tourist island of Bohol earlier this month.
In separate attacks, at least 10 members of the terror group have been killed in the island province
in the last month. At least three more militants are still at large, according to CNN affiliate CNN Philippines.
The attackers were part of a group of ASG militants who sailed to Bohol earlier in April, CNN Philippines reported.
The fighters' presence in Bohol, an island in the south of the Philippines archipelago, marks a expansion for the group -- traditionally its activities have been confined to the Muslim-majority islands of Mindanao and Sulu, to the south of Bohol.
Duterte took power in June and has waged an all-out "war on drugs," which killed some 6,000 people in his first six months.
In December, Duterte admitted to having killed suspected criminals
when he was mayor of Davao City.
He spoke Monday at the opening ceremony of the 2017 Palarong Pambansa in San Jose de Buenavista, Antique province.
Addressing students, coaches and technical officials from the 18 regions of the country, the President urged them to build competitiveness, fairness, values and a sense of goodwill as they participate in the annual sporting event.
Speaking of terrorists, he said:
"They are animals. If you want me to be an animal I can be one. I can be the same. I can dish it more than what you can. Fifty times more than you can."