A terrorist group in the Philippines has killed John Ridsdel, the 68-year-old Canadian kidnapped last September – an execution Prime Minister Justin Trudeau called "cold-blooded murder" and the man's family said was "senseless."

A second Canadian, 50-year-old Robert Hall, remains captive, a Canadian government official confirmed.

Mr. Ridsdel was a world traveller who had made the Philippines his home. He was a passionate sailor, experienced in living and travelling in conflict areas, and a father of two adult daughters.

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He was held for a ransom by the terrorist organization Abu Sayyaf and beheaded after the deadline passed.

"Our family is devastated at the loss of our father and brother John Ridsdel whose life was cut tragically short by this senseless act of violence despite us doing everything within our power to bring him home," the Ridsdel family said in a statement Monday.

"John was a kind and gregarious person who touched everyone he knew with his enthusiasm and generosity. He loved life and lived it to the fullest with his family and friends at the centre."

"He was loved by all his friends and adored by his daughters, sister, and extended family. He will be sorely missed for all our days to come."

Mr. Trudeau, speaking to reporters in Kananaskis, Alta., said his government will work with the Philippines to bring justice to the alleged killers.

"This was an act of cold-blooded murder and responsibility rests squarely with the terrorist group who took him hostage," Mr. Trudeau said.

Mr. Ridsdel and Mr. Hall were kidnapped on the resort island of Samal in the southern province of Davao del Norte last fall. Other captives include a Norwegian man and a Filipina. A member of the Hall family declined to comment. Another did not return a call seeking comment.

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Bob Rae, the former Ontario premier and member of Parliament, has known Mr. Ridsdel since 1966, when they started at the University of Toronto together.

"He wasn't someone who was going to spend his days at a country club or watching golf on television," Mr. Rae said in an interview. "That was not John. … He was definitely an adventurer."

Mr. Rae said he had been trying to help the Ridsdel family "navigate" the situation. "People tried hard. His family tried very, very hard and did a lot to try to respond," the former politician said.

Canada has a policy against paying ransoms, according a government official.

Abu Sayyaf, the jihadi group that allegedly killed Mr. Ridsdel, emerged as part of an ethnic conflict in the Philippines, according to Will Plowright, a doctoral candidate in the department of political studies at the University of British Columbia. Abu Sayyaf, however, has pledged allegiance to Islamic State, although Mr. Plowright said the two organizations "have no real connections."

Before Mr. Ridsdel went missing, he was about to join a sailing rally between the Philippines and Indonesia's Sulawesi and West Papua. He missed the start of the rally and his boat remained at the marina in the southern Philippines that served as the rally's starting point. Gunmen attacked the facility in September, 2015.

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Bill Bowen, a fellow sailor who met Mr. Ridsdel through work in the 1980s, last visited him in the Philippines about five years ago. "He's the last person on Earth that you'd expect to find involved in what was happened," Mr. Bowen said. "[He was] very mild-mannered, very polite, very inoffensive person and not in any way aggressive or threatening."

Moreover, Mr. Ridsdel was a savvy traveller. He worked in Algeria during times of conflict and was aware of the tensions in the Philippines, Mr. Bowen said. "This is somebody who is fairly clued up and you wouldn't really expect to fall … into a trap."

Mr. Ridsdel was an award-winning journalist turned oil-and-mining executive. His overseas assignments with Petro-Canada included stints in Pakistan, Myanmar and Algeria. He landed in the Philippines after joining Calgary-based TVI Pacific Inc., a mining company. He was semi-retired and working as a consultant for the mining company before he was kidnapped.

Mr. Hall, meanwhile, had recently begun dating a Filipina, Maritess Flor, who had accompanied him for part of a cross-Pacific sailboat journey – and whose family grows sugarcane not far from the marina where gunmen seized the Canadians from their yachts, along with Ms. Flor and Norwegian Kjartan Sekkingstad. Mr. Sekkingstad lived for a time in Canada and carries a Canadian passport, friends have told The Globe and Mail.

For the community around Ms. Flor, the lack of information in recent months has raised suspicions that the military has failed in its efforts to free those taken captive.

"I think they tried but weren't successful, so that's why there's been a news blackout, because it won't look good for the Philippine government," said Val Araneta, a leader in the community where Ms. Flor's family lives.

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"I'm disappointed with the government," he said.

Ms. Flor's family, he said, has been "stressed and depressed" through the ordeal.

On Monday evening, during a power outage in the Philippine municipality of Jolo, two men on motorcycles threw a plastic bag into a square near the town's municipal offices and police station.

Children playing nearby initially ran from the bag, believing it to be a bomb, said Dr. Raden Ikbala, a local physician. But when "they opened it, they saw the head of a man," he said, and reported it to police.

Such tactics have been used before by local militants.

"Sometimes they throw the heads in public places so that it will be discovered," said Dick Gordon, a Philippine senator who had been asked several months ago to negotiate the release of the hostages. He said it appears "he was executed because of the failure to pay the ransom" – although none of the circumstances are clear.

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The men on the motorcycle, Mr. Gordon said, left a chilling message as they departed.

"They threw it, and they said, 'We will be back.' We don't know why they said that."

With a report from Steven Chase in Kananaskis, Alta.