OTTAWA -- The RCMP is conducting a criminal investigation into the murder of hostage John Ridsdel in the Philippines.

The Mounties are relying on the extraterritorial provisions of the Criminal Code in pursuing the overseas investigation, a senior official says.

It means the perpetrators, if found and charged, could one day face justice under Canadian law.

The official spoke with The Canadian Press on condition of anonymity given the sensitivity of the ongoing hostage case.

Ridsdel, 68, of Calgary, was beheaded earlier this week after a large ransom demand from his captors, members of the Abu Sayyaf militant group, went unmet.

Police forensic experts were trying Wednesday to determine if the headless body of a Caucasian man that was found by villagers in the southern Philippines was that of Ridsdel.

Canadian Robert Hall, abducted with Ridsdel from a marina in September, is still being held along with several others.

Prime Minister Justin Trudeau said this week that the Canadian government will not pay a ransom -- directly or indirectly -- to a terrorist group.

The senior official reiterated Wednesday that there is "no sort of government negotiation" taking place.

If there was a reasonable prospect of mounting a successful rescue mission, it would happen, added the source. "All of those things have been examined, weighed and fleshed out."

However, there are serious obstacles, not the least of which is the challenging island and jungle terrain where the hostages are said to be held. "The stark reality is that that's some pretty impenetrable geography there."

In addition, unlike with previous hostage-takings in the Sahel and Afghanistan, there is little in the way of existing logistical support to bolster a rescue effort, the official said.

"It's a very complicated and dangerous situation."

Retired Brig.-Gen. James Cox, who served around the world during a 35-year military career, doesn't envision Canada's special forces swooping in to attempt a rescue.

"I don't see that we have the ability to do that. I don't know that we would want to do that in another sovereign state," he said in an interview.

"I don't think there is anything that you're able to do other than help the police and the forces of the sovereign state involved as best as you can, and as best as they have requested."

-- With files from The Associated Press