The Philippine army says Abu Sayyaf fighters have beheaded one of four Filipino fishermen they took captive in December.

Brigadier-General Cirilito Sobejana, military commander on the southern island of Jolo island, said on Sunday the boat's captain had been executed in the jungle near the town of Patikul on Thursday but that his remains had yet to be recovered.

Noel Besconde was abducted along with three crewmen by the Abu Sayyaf group, which has ties to the Islamic State of Iraq and the Levant (ISIL) group, in December while on board a fishing vessel in the Celebes Sea.

Abu Sayyaf is a small group known for beheadings, kidnappings, bombings and extortion in the south of the mainly Catholic country.

Sobejana said it was possible the abductors beheaded Besconde because he was sick and had become a liability

"The reason why he was beheaded is that he was delaying their movement," Sobejana said. "They [Abu Sayyaf fighters] are highly mobile and we are pursuing them."

Troops have not yet found Besconde's body, but Sobejana said the military received a video of the beheading.

Sobejana said the group had demanded about $60,500 as ransom for Besconde's release but the government maintains its policy of refusing to pay ransom.

The Philippine army has declared all-out war against Abu Sayyaf on the islands of Jolo and Basilan, but is constrained by the group's presence among large civilian communities.

Rooted in separatism

Abu Sayyaf has its roots in separatism, but its activities are mostly banditry and piracy. It has invested the profits of its business in modern weapons and fast boats.

Sobejana said Abu Sayyaf is still holding Besconde's crew, along with more than a dozen foreign nationals in Jolo, which is the primary island of the province of Sulu.

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The group last year beheaded Canadians John Ridsdel and Robert Hall. An elderly German, Jurgen Kantner, suffered the same fate in February when a $600,000 ransom demand was not paid.

The army said on Wednesday that an Abu Sayyaf leader who was directly involved in the kidnapping and execution of the Ridsdel and Hall was among those was killed by Philippine troops during clashes last weekend on a resort island.