Members of the Abu Sayyaf Group have pledged allegiance to the Islamic State. Video grab/File

MANILA - Filipino troops have killed about 40 Abu Sayyaf rebels in offensives on southern islands over the past week, the military said on Monday, as a new government intensifies operations to wipe out one of Asia's most formidable kidnap gangs.

Battles on Basilan and Sulu islands since Wednesday killed one soldier and also wounded some two-dozen members of the al Qaeda-linked Islamist group, which gained in notoriety over the past few months with its beheading of two Canadian hostages.

"A heavy firefight was still ongoing involving armored vehicles, artillery fire and close-air support," Filemon Tan, spokesman of the Western Mindanao Command, told journalists, citing intelligence reports received late on Sunday.

Abu Sayyaf, 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 kidnap rackets.

The rebels are 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 if Abu Sayyaf rebels were responsible.

Security experts say the rebels are motivated less by Islamist ideology and more by the tens of millions of dollars from kidnappings. They use the money to finance the purchase of automatic weapons, grenade launchers, fast boats and high-tech navigational equipment.

The government of President Rodrigo Duterte, who took office on June 30, is under renewed pressure to tackle Abu Sayyaf following the decapitation of the two Canadians and the kidnapping of Indonesian sailors.

His new defense minister recently said killing off Abu Sayyaf was his top security priority, taking precedence over the disputed South China Sea in terms of budget allocation.