Robert Hall and John Ridsdel are believed to have been killed by Abu Sayyaf militants (AP)

Philippine officials have confirmed that Abu Sayyaf militants have beheaded a Canadian man, the second Canadian hostage killed by Abu Sayyaf militants in two months after their demands for a large ransom were not met.

Robert Hall was abducted from a marina last September with another Canadian, a Norwegian and a Filipino. The other Canadian, former mining executive John Ridsdel, was beheaded in April.

Presidential spokesman Herminio Coloma condemned "the brutal and senseless murder" of Mr Hall. He had been held by Abu Sayyaf in the jungle in southern Sulu province for nine months.

The government has vowed to end the militants' "reign of terror".

Mr Coloma said: "This latest heinous crime serves to strengthen our government's resolve to put an end to this reign of terror and banditry."

A militant video obtained by Philippine police officials showed Mr Hall in an orange shirt kneeling in front of a black Islamic State-style flag before he was killed in a jungle area.

An Abu Sayyaf deadline for the payment of a large ransom passed on Monday and police later found the severed head of a Caucasian man outside a Roman Catholic cathedral in Sulu province's main Jolo town.

In Ottawa, Canadian prime minister Justin Trudeau said there was "compelling reason to believe" Mr Hall had been killed by his captors, and that the Canadian government was working with Philippine authorities to confirm his death.

"We have every reason to believe that the reports are unfortunately true," Mr Trudeau said.

He added he was "horrified" by the killings and reaffirmed Canada's refusal to pay ransoms.

"The government of Canada will not and cannot pay ransoms for hostages to terrorist groups, as doing so would endanger the lives of more Canadians," Mr Trudeau said in a statement.

"We are more committed than ever to working with the government of the Philippines and international partners to pursue those responsible for these heinous acts and bring them to justice, however long it takes."

He recently urged leaders of other members of the G7 to reiterate their opposition to paying ransoms.

After being abducted from the marina on southern Samal Island last September, the hostages were taken by boat to Sulu, where Abu Sayyaf has held hostages for years in mountainous jungle camps.

Mr Ridsdel was beheaded on April 25 after a ransom demand of 300 million pesos (£4.5 million) was not paid.

In an Abu Sayyaf video posted on YouTube after Mr Ridsdel's death, Mr Hall and the two other hostages, Norwegian Kjartan Sekkingstad and Filipino woman Marites Flor, pleaded to Canadian and Philippine officials to negotiate their release.

"We live like this every day, go to bed like this," Mr Hall said, raising his arms to show he was handcuffed. "We have a hundred people heavily armed around us all the time that dictate to us and talk to us like children. We've been humiliated in every way possible. One of us has already been murdered."

Mr Hall spoke later in the video for a second time, sounding resigned to a tragic fate.

"I would also like to thank my family for the effort they put in - my family and friends for the effort they put in - to get me out of here. I know you did everything you can, and I truly appreciate it. I'm sorry I got you in this mess," he said.

Mr Trudeau extended his "heartfelt condolences" to Mr Hall's relatives and friends.

The US and the Philippines have both listed Abu Sayyaf as a terrorist organisation for kidnappings, beheadings and bombings. The group emerged in the early 1990s as an extremist offshoot of a decades-long Muslim separatist rebellion in the country's south.