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The Philippine military came under increased pressure Tuesday to rescue more than 20 foreign hostages after their Muslim extremist captors beheaded a Canadian man, but troops face a dilemma in how to succeed without endangering the remaining captives.

Abu Sayyaf gunmen beheaded John Ridsdel on Monday in the southern province of Sulu, sparking condemnations and prompting Canadian Prime Minister Justin Trudeau to pledge to help the Philippines pursue the extremists behind the "heinous act."

"Canada condemns without reservation the brutality of the hostage takers and this unnecessary death," Trudeau told reporters. "This was an act of cold-blooded murder and responsibility rests squarely with the terrorist group who took him hostage."

Ridsdel's head, which was placed in a plastic bag, was dumped by motorcycle-riding militants Monday night in Jolo town in impoverished Sulu, a densely forested province about 950 kilometers (590 miles) south of Manila, where the Abu Sayyaf and allied gunmen are believed to be holding 22 foreign hostages from six Western and Asian countries.

It's a politically sensitive time for troops to carry out major offensives, at the height of campaigning in a closely fought race among four contenders in the May 9 presidential election. President Benigno Aquino III and opposition politicians have had differences over the handling of the Muslim insurgency and the social ills that foster it.

"The pressure on the armed forces is really immense," said Julkipli Wadi, who has conducted extensive studies on the Muslim secessionist conflict in the south.

The underfunded military has to contend with escalating territorial disputes in the South China Sea while dealing with Muslim and Marxist rebellions that have endured through several presidencies, fueled by the poverty, neglect and desperation that have not been tamed by political leaders, Wadi said.

A large-scale offensive could displace many villagers and draw attention to the longstanding security and social issues in the vote-rich south, homeland of minority Muslims in the largely Roman Catholic nation.

That could play to the advantage of Rodrigo Duterte, the tough-talking city mayor from the south who has emerged as the front-runner in the presidential race with a lofty promise to end crime in six months and restore law and order. Aquino has endorsed another candidate, Mar Roxas, whose platform focuses on continuing the president's anti-corruption drive and economic reforms. All the presidential candidates condemned the beheading.

The Philippine military and police said "there will be no letup" in the effort to combat the militants and find the hostages, even though they have had little success in safely securing their freedom. Many hostages were believed to have been released after huge ransom payments.

"The full force of the law will be used to bring these criminals to justice," they said in a joint statement.

About 2,000 military personnel, backed by Bell UH-1 "Huey" and MG520 rocket-firing helicopters and artillery, are involved in the manhunt for the militants, who are believed to be massing in Sulu's mountainous Patikul town, military officials said.

While under pressure to produce results, government troops have been ordered to carry out assaults without endangering the remaining hostages, including in the use of airstrikes and artillery fire, a combat officer told The Associated Press by cellphone from Sulu. He spoke on condition of anonymity because he was not authorized to talk to reporters.

Amid the offensive, Brig. Gen. Alan Arrojado resigned Tuesday in Sulu as commander of an army brigade "due to conflict of approach in addressing the Abu Sayyaf threats" in the province. Arrojado did not elaborate.

In past militant videos posted online, Ridsdel and fellow Canadian Robert Hall, Norwegian Kjartan Sekkingstad and Filipino Marites Flor were shown sitting in a clearing with heavily armed militants standing behind them. In some of the videos, a militant aimed a long knife at Ridsdel's neck as he pleaded for his life. Two black flags with Islamic State group-like markings hung in the backdrop of lush foliage.

The four were seized from a marina on southern Samal Island and taken by boat to Sulu, where Abu Sayyaf gunmen continue to hold several captives, including a Dutch bird watcher who was kidnapped more than three years ago, and Indonesian and Malaysian crewmen who were snatched recently from three tugboats.

Ridsdel was killed after the militants failed to receive a huge ransom demand by a Monday deadline. A police official said the killing of five and wounding of about 16 Abu Sayyaf gunmen in a military assault three days before the beheading may have angered the extremists and helped lead them to decide to kill him in revenge.

In Canada, Ridsdel was remembered as a brilliant, compassionate man with a talent for friendship.

"He could bridge many communities, many people, many situations and circumstances and environments in a very gentle way," said Gerald Thurston, a lifelong friend of the former mining executive and journalist who grew up with him in Yorkton, Saskatchewan.

Thurston said Ridsdel is survived by two adult daughters from a former marriage.

The Abu Sayyaf began a series of large-scale abductions after it emerged in the early 1990s as an offshoot of a separatist rebellion by minority Muslims in the southern Philippines.

It has been weakened by more than a decade of government offensives, but has endured largely as a result of large ransom and extortion earnings. The United States and the Philippines have both listed the group as a terrorist organization.