Philippine troops have killed 40 Abu Sayyaf Group fighters and wounded 25 others, in two battlefronts on the southern islands of Mindanao during the first major operation under the new President Rodrigo Duterte.

Regional military spokesman Major Filemon Tan said on Monday that 22 fighters had been killed and 16 others wounded in assaults that started last week in the jungles of Jolo in the southern Sulu province. One soldier had been killed in the fighting.

Tan said another 18 Abu Sayyaf fighters had been killed and nine others wounded in simultaneous offensives on the nearby island province of Basilan.

Philippines: Abu Sayyaf frees 10 Indonesian captives

President Duterte, who started his six-year term on June 30, has warned the Abu Sayyaf group to stop a wave of ransom kidnappings, saying he will eventually confront them.

His military chief said last week a looming offensive would "shock and awe" the group, which has pledged allegiance to the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), and was previously with al- Qaeda.

The group has gained notoriety in recent months with its beheading of two Canadian hostages.

Abu Sayyaf, a group whose name translates as "Bearer of the Sword", has dogged successive Philippine governments, entrenching its network with vast sums of ransom money in what has become one of Asia's most lucrative kidnapping rackets.

In April at least 19 soldiers were killed following an attack by the armed group.

The group is still holding at least 14 hostages - one Dutch, one Norwegian, five Filipinos and seven Indonesians.

Three Indonesians were abducted from a tugboat on Sunday, although it was not immediately clear whether Abu Sayyaf rebels were responsible.

On Monday, Indonesian Foreign Minister Retno Marsudi called on the Philippines and Malaysia to do more to their "unsafe" waters.

"This kind of incident cannot be tolerated at all," Marsudi said. "Serious efforts, I repeat, serious efforts, must be taken immediately both by the Philippine and Malaysian governments."

According to security experts, the Abu Sayyaf fighters are motivated less by Islamist ideology and more by the tens of millions of dollars they have earned from kidnappings. The money is used to finance the purchase of automatic weapons, grenade launchers, fast boats and hi-tech navigational equipment.

The Duterte government is under renewed pressure to tackle Abu Sayyaf following the decapitation of the two Canadians and the kidnapping of Indonesian sailors.

Duterte's new defence minister recently said the killing of Abu Sayyaf was his top security priority, taking precedence over the disputed South China Sea in terms of budget allocation.