MANILA (Reuters) - The Philippines will send an additional 2,500 troops to a remote southern island this week as the army steps up an offensive against the Islamic State-linked Abu Sayyaf, a presidential spokesman said on Tuesday.

About 45 soldiers and Muslim rebels have been killed on Jolo island since Thursday when the army launched an air-and-ground assault on the main base of the militants after President Rodrigo Duterte ordered the Abu Sayyaf to be "destroyed".

"We are going full force, launching an all-out operation against the Abu Sayyaf there," presidential spokesman Ernesto Abella told reporters. "We are adding five battalions or about 2,500 people."

The Abu Sayyaf 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.

(Reporting by Manuel Mogato; Editing by Nick Macfie)