Abu Sayyaf is linked to the global Islamist militant organisation Al Qaeda.
The terrorists called Analiza Lingayan, the captive's wife, Sunday night and told her that "they were not going to decapitate her husband, as planned before, out of respect for Ramadan", according to Philippine Star.
The deadline given by the captors to the Lingayan family to pay a ransom of three million pesos ($68,719) -- 17 million less than what they claimed after abducting 50-year-old Remigio June 4 from the island of Jolo -- ended Sunday.
On Saturday, Philippine authorities tightened security in the southern part of the country due to a "possible terrorist threat" from Abu Sayyaf.
This insurgent group was established by a few ex-fighters of the Afghanistan war against Soviet Union in 1991 and since then the group has carried out some of the bloodiest attacks and kidnappings in the country.
In addition, it has collaborated with Yemma Islamiya, an arm of the Al Qaeda in southeast Asia.