Last week government troops killed Binang Sali, considered a spiritual leader of the group accused of kidnapping and beheading tourists, and carrying out deadly bomb attacks.
 
Leadership vaccum
 
Lieutenant-Colonel Bartolome Bacarro, a military spokesman, said on Thursday: "Right now, they are suffering from a leadership vacuum and they are now disorganised. We will keep up the tempo."
 
Last week, the Philippines signed a convention on counter-terrorism with its South-East Asian neighbours during the Association of South-East Asian Nations summit.
 
Arroyo said the agreement would "tighten the dragnet and stop the movement of terrorists, their finances and their deadly material across the seas and borders".
 
Held responsible
 
Abu Sayyaf has only about 400 core members, but it has been held responsible for the Philippines' worst terrorist attack, the bombing of a ferry near Manila Bay in 2004 that killed at least 100 people.
 
The group is said to have links with Jemaah Islamiyah, which is believed to be fighting for a pan-Asian Islamic state, and also with al-Qaeda.
 
Al Jazeera's Veronica Pedrosa says now that Abu Sulaiman been killed, the Philippine military is warning that there may be revenge attacks.
 
The group originally broke off from larger separatist armies, fighting for an independent Muslim homeland in the mostly Christian Philippines.
 
Lucrative racket
 
The Abu Sayyaf became less interested in the cause than in lucrative kidnapping operations, Pedrosa said.
 
They are also believed to have strong links with al-Qaeda linked Jemaah Islamiyah.
 
Abu Sulaiman is only one face, however, in the gallery of the Philippines' most wanted.
 
The top leader of the group is Khadaffy Janjalani.
 
The Philippine military think they may have killed him in September, but results of DNA tests haven't been announced yet, Pedrosa said.