US military advisers have been helping to train the Philippines military to fight them.
Abu Sayyaf was once linked to regional Islamist networks, but has recently become better known for criminal brutality and high-profile kidnappings, mostly targeting Christians and foreigners.
In January, militants kidnapped three staff members of the International Committee of the Red Cross.
Two were freed in April, while the last hostage, 62-year-old Italian Eugenio Vagni, was released in July after being held for nearly six months.
The troops "launched a decisive law enforcement operation targeting the Abu Sayyaf's main training camp in the province", said army spokeswoman Lt Steffani Cacho.
She said "sizeable quantities" of bombs were found, some already "rigged to explode".
The army's losses were the highest in a single day's combat for some years.
The fighting was a "slugfest", said Maj Gen Dolorfino. "It was really close-quarter fighting so we couldn't use our artillery," he told AP.
The south of the Philippines remains vulnerable to fatal violence and tens of thousands of civilians have been displaced by the fighting.
Analysts say this is due to the government's failure to deliver on promises of resource-sharing and development aid, the military's lack of professionalism, and rebel groups' refusal to give up a lifestyle of resistance.
While Abu Sayyaf is largely a criminal gang, two other groups have pursued political autonomy or independence for Mindanao for decades.
The Moro National Liberation Front first appeared in the early 1970s, fighting for an independent Moro nation. A 1996 autonomy deal faltered amid renewed violence in 2005 and 2007.
The Moro Islamic Liberation Front (MILF) is a more militant rebel group, which split from the MNLF in 1977.
In November 2007, the Philippine government said it had reached an agreement with the MILF on the boundaries for a Muslim homeland.
But the Supreme Court ruled that the draft agreement was unconstitutional. The failure of the negotiations prompted renewed fighting, which by mid-October 2008 had displaced 390,000 people, according to the International Crisis Group.
The New People's Army, the military wing of the Communist Party of the Philippines (CPP), has also been active in the south. Peace talks are due to resume, again, later this month.
Analysts have said they believe President Gloria Arroyo lacks the will or authority to achieve a breakthrough in any proposed negotiations with such long-standing insurgencies.
She is dependent on the military for political support, parts of which have a stake in continued fighting.
Although the country's constitution bars the presence of foreign military bases on Philippine soil, the United States provides military training and equipment, and has a revolving presence of at about 500 troops on the ground in the South.
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