Ridsdel was beheaded by Islamist militant group Abu Sayyaf
, which took him hostage in September, along with three others.
Aquino added there was an opportunity to "smash" the group, which had allegedly plotted to kidnap members of his family, as well as Filipino boxing legend Manny Pacquiao or his relatives.
"Our reports tell us that the captives are under the control of (leader Raddulan Sahiron), who has consolidated his forces around himself and the captives," President Benigno Aquino said in a statement detailing the group's atrocities.
"This presents both a problem and an opportunity. It is a problem because of the sizable force surrounding (Sahiron) and the captives, but it is also an opportunity because smashing these forces is within our grasp."
Sahiron became the overall leader of Abu Sayyaf in 2005.
"Even as it poses as a group of Islamic freedom fighters ... Abu Sayyaf has behaved as criminals focused on enriching themselves by taking hostages for ransom," Aquino said.
Ridsdel has been described as a "kind and gregarious person who touched everyone he knew with his enthusiasm and generosity."
In a statement
, Ridsdel's family said he "loved life and lived it to the fullest with his family and friends at the center. He was loved by all his friends and adored by his daughters, sister and extended family."
"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."
Bob Rae, a close friend of Ridsdel, said "lots of effort" was made to respond to ransom demands but the amounts asked for were too high.
A former Canadian Member of Parliament, Rae told CNN that he "was a very vital and engaging guy."
Ridsdel had worked as a reporter for The Calgary Herald and CBC, and eventually retired from TVI Pacific to tour the world.
"He was very adventurous, his career path was unique to him," Rae said.
Canadian Prime Minister Justin Trudeau said Ridsdel's death was "an act of cold-blooded murder and responsibility rests squarely with the terrorist group who took him hostage."
Trudeau said Canada condemns the "brutality" of this "unnecessary death," and expressed his "deepest condolences" to Ridsdel's family and friends.
Philippines security forces vowed that "the full force of the law will be used to bring these criminals to justice."
"There will be no let up in the determined efforts ... to neutralize these lawless elements and thwart further threats to peace and security," the armed forces of the Philippines and the Philippine national police said in a joint statement.
Ridsdel was among four people abducted September 21
at the Oceanview Resort on Samal Island, which lies off the coast of the major southern island of Mindanao, Philippine officials said
This part of the southern Philippines is home to Abu Sayyaf, an Islamist militant group that's been linked to al Qaeda and ISIS
. The separatist group has at times preyed on foreigners in recent years, taking them hostage to further its aims.
The situation has drawn growing political attention in the country. Earlier this month, one lawmaker called for
Abu Sayyaf to be a topic in the country's next presidential debate.
In addition to Ridsdel, Norwegian national Kjartan Sekkingstad, Canadian national Robert Hall and Filipina Marites Flor were also taken hostage, according to officials
In a statement
, Norwegian Foreign Minister Borge Brende said Norway would "continue our ongoing efforts to find a solution for the remaining hostages."