The video, released Sunday, anticipates a rapidly-expiring June 13 deadline set by the group, which is headquartered in the restive Muslim-majority province of Mindanao in the country's far south.
The video echoes previous videos released by the group, and shows Norwegian national Kjartan Sekkingstad, Canadian national Robert Hall and Filipina Marites Flor.
The video opens with Flor, wearing a headscarf, addressing Duterte, who won the country's presidential election in early May, in a local dialect, according
to jihadist monitoring group SITE Intelligence. It then focuses on Hall, who also addresses the president-elect.
He accuses the Canadian government of abandoning him and his family during the ordeal, and entreats him to "negotiate or communicate with them" through an intermediary named "June" at the Canadian embassy, according to a transcript released by SITE.
He does not elaborate on the identity or the role of the embassy contact he names.
Hall then describes their humiliating, fear-filled daily existence.
"We live like this every day, go to bed like this. We have a hundred people heavily armed around us all the time that dictate to us and talk to us like children," he says.
"We've been humiliated in every way possible. One of us has already been murdered. We hope that you can work on our behalf as soon as possible to get us out of here. Please, the sooner the better. We're three-quarters dead right now."
He later thanks to his family and friends for their efforts to free him and apologizes for the "mess" he got them in.
Sekkingstad speaks next, appealing to his own government alongside the Canadian and Filipino governments, as well as its incoming president.
"Please try to help us. Contact this group through June at the Canadian embassy and try to negotiate with this group," he says.
"We will (be) executed on June 13 at 3 o'clock, unless there is an agreement made with this group."
In April, after murdering Canadian hostage John Ridsdel
who was captured alongside the surviving hostages in September of last year, the group reset the deadline to June 13 for the remaining three hostages.
The group had earlier demanded a $6.37 million ransom (Php 300 million) for each of the victims to be paid by April 25, Philippines state media reported
The four were taken in a raid on the Oceanview Resort on Samal Island which lies off the coast of the major southern island of Mindanao. Hall, Ridsdel and Flor were visiting the resort's marina on their yacht, while Sekkingstad was the manager of the property.
In the latest video both the remaining male hostages are pictured wearing orange t-shirts, mirroring ISIS' gruesome hostage videos, in which captives, particularly Western ones, are forced to wear orange jumpsuits in a grim reference to captives at the U.S.' controversial military prison in Guantanamo Bay in Cuba.
Last month, 10 Indonesian hostages were released
by Abu Sayyaf, and several days later four remaining Indonesians were freed.
Who are Abu Sayyaf?
The violent extremist group seeks to establish an independent Islamic state on Mindanao, the southernmost major island of the predominantly Catholic Philippines.
The Philippines military has made inroads in recent years in thwarting the group's terrorist bombing campaigns, prompting a shift in focus by the group to kidnappings for ransom.
Greg Poling, director of the Asia Maritime Transparency Initiative at the Washington-based Center for Strategic International Studies, has said that "after about 15 years of a pretty harsh crackdown by the U.S. and the Philippines, what they've basically become is a criminal group made up of a few hundred who engage in extortion and kidnapping."