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.
'Devastated'
Ridsdel has been described as a "kind and gregarious person who touched everyone he knew with his enthusiasm and generosity."
"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.
'Cold-blooded murder'
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.
Other hostages
CNN's Richard Beltran contributed to this report. CNN Philippines also contributed reporting.