Philippine authorities on Tuesday confirmed that Muslim extremist guerrillas had beheaded a second Canadian hostage, as they defended their inability to save him despite months of pursuit.

"We strongly condemn the brutal and senseless murder of Mr Robert Hall, a Canadian national, after being held captive by the Abu Sayyaf group in Sulu for the past nine months," presidential spokesman Herminio Coloma said in a statement.

A military statement also confirmed that a severed head, believed to be Hall's, was found near the Jolo island cathedral Monday night.

"The discovery confirmed the brutal beheading by the evil, criminal ASG (Abu Sayyaf group) of a kidnap victim," the statement added.

Earlier, Canadian Prime Minister Justin Trudeau declared that his government has "every reason to believe" that Hall had been killed by the Abu Sayyaf, the second Canadian captive to be slain this year.

Members of the notorious kidnap-for-ransom Abu Sayyaf gang had said they would murder Hall if they did not receive 300 million pesos ($6.5 million) ransom by Monday afternoon.

Hall was among four people abducted in September last year from aboard yachts at a tourist resort on Samal island in the southern Philippines.

Another Canadian kidnapped at the same time, John Ridsdel, was beheaded in April after a similar ransom demand of 300 million pesos was not paid.

The fates of the two other people abducted at the Samal resort -- Hall's Filipina girlfriend Marites Flor and Norwegian resort manager Kjartan Sekkingstad -- were not known.

The beheadings have taken place despite the heavy deployment of military and police forces to locate them in the strife-torn island of Jolo, the largest island in the Muslim-populated archipelago of Sulu, about 1,000 kilometres (620 miles) from Manila.

Major Filemon Tan, spokesman of military forces in the south, said Tuesday that the kidnappers were evading military pursuers with the help of the impoverished Muslim residents of the island.

"They have relatives in the community. They are the ones that give them a warning when there are soldiers in the area," he told radio station DZMM.

He also said the island's forested, hilly terrain, a broad coastline that allows for swift movement by boat and the kidnappers' tactic of breaking up into smaller groups, were all hindering pursuit.

"But we are studying this deeply and I can say we are adjusting and it will be a matter of time that we will hit them also," he added.

Listed by the United States as a terrorist organisation, the Abu Sayyaf is a loose network of Islamic militants that was founded in the early 1990s with money from Osama bin Laden's Al-Qaeda network.

Its leaders have in recent years declared allegiance to the Islamic State group that holds territory in Iraq and Syria.