"Casualties are to be expected. But what has to be of utmost importance is neutralising the criminal activities of the ASG," Aquino said in a statement, referring to the Abu Sayyaf militant group by a commonly used acronym.
Aquino released the statement after the severed head of Canadian John Ridsdel, kidnapped seven months ago from aboard a yacht, was dumped Monday on a street on Jolo, a remote southern island that is one of the Abu Sayyaf's main strongholds.
"This murder was meant to terrorise our whole population. The Abu Sayyaf thought they could instill fear in us. Instead, they have galvanised us even further to ensure justice is meted out," Aquino said.
"We have always been open to talks with those who desire peace, but those who commit atrocities can expect the full might of the state."
He did not give a timeframe for the assault.
The Abu Sayyaf militants, whose leaders have pledged allegiance to the Isis terror group, are holding more than 20 other foreigners captive. In addition to Sekkingstad, these include another Canadian and a Filipina who were abducted at the same time as Ridsdel at a marina near Davao, the biggest city in the southern Philippines and about 600 kilometres (370 miles) from Jolo.
The Abu Sayyaf is also believed to be holding a Dutch birdwatcher kidnapped from a southern Philippine island in 2012, as well as 18 Indonesian and Malaysian sailors abducted over the past month.
Aquino said the captives were under the control of Radullan Sahiron, one of the Abu Sayyaf's founders who is famous for losing one arm in battle against the military.
Norway: 'Abhorrence and outrage'
The Norwegian government released a statement on Tuesday condemning Ridsel's murder.
Abhorrence and outrage is the only reasonable response to his murder by the terrorist group Abu Sayyaf,' said Minister of Foreign Affairs Børge Brende.
Unlike Canadian PM Justin Trudeau, who said unequiviocally on Tuesday that Canada will not pay a ransom, the Norwegian government did not directly address the terrorists' demands.
"Our thoughts and sympathy go to John Ridsel's family and friends. And we must not forget that three other hostages are still being held, and that their families and friends are also suffering. Norway will persist in its efforts to find a solution for the remaining hostages," said Brende.
'Smash' the Abu Sayyaf
Aquino said Sahiron had consolidated his forces around himself and the captives in Sulu, a small Muslim-populated archipelago about 1,000 kilometres from Manila. Jolo is the biggest island in Sulu.
"This presents both a problem and an opportunity. It is a problem because of the sizeable force surrounding Sahiron and the captives, but it is also an opportunity because smashing these forces is within our grasp," Aquino said.
The Abu Sayyaf is a radical offshoot of a Muslim separatist insurgency in the south of the mainly Catholic Philippines that has claimed more than 100,000 lives since the 1970s.
It is believed to have just a few hundred militants but has withstood repeated US-backed military offensives against it, surviving by using the mountainous, jungle terrain of the southern islands to its advantage.
Although the Abu Sayyaf's leaders have pledged allegiance to Isis, analysts say they are mainly focused on their lucrative kidnappings-for-ransom rather than setting up an Islamic caliphate.
Abu Sayyaf gangs have earned many millions of dollars from kidnapping foreigners and locals since the early 1990s.
One of the Abu Sayyaf's biggest recent windfalls is believed to have come in 2014 when it claimed to have been paid more than $5 million for the release of a German couple abducted from aboard their yacht in the southwest Philippines.
Manny Pacquaio kidnap plot
Aquino also revealed a series of alleged Abu Sayyaf plots to kidnap Filipino boxing hero Manny Pacquiao and the president's younger sister, Kris, a popular television personality.
He said Isnilon Hapilon, who Isis has recognised as a local Filipino leader, was behind these plots and wanted to conduct the kidnappings, conduct bombings in Manila and even assassinate himself so that Isis would give them funds and resources.
He reassured the public that key leaders involved in these plots had been arrested and those threats had been put "to bed".
However he also said Hapilon was on Basilan island, the other key Abu Sayyaf stronghold neighbouring Jolo, and that military assaults against him were continuing.
On April 9, 18 Filipino soldiers were killed as they waged a day-long battle against Abu Sayyaf gunmen on Basilan.
Also Wednesday, the Philippines said it was considering launching joint sea patrols with Malaysia and Indonesia in the waters where the recent kidnappings of the sailors occurred.