The fighters were believed to have been avenging the death of Parad, Lieutenant Cacho said.
However, Antonio Mendoza, the Basilan police chief, said the attack had been motivated by a personal grudge with the village chairman.
In critical condition
Seventeen people were wounded in Saturday's attack, with nine in a critical condition, four of them children, Dr Kadil Jojo Sinolinding, the regional health chief, told The Associated Press news agency.
"Most of the victims were still asleep when they were strafed and then their houses were torched"
Dr Kadil Jojo Sinolinding, regional health chief
"Most of the victims were still asleep when they were strafed and then their houses were torched," he said.
The pre-dawn raid was the country's worst attack on civilians in nine years.
The military is searching for the attackers but there have been no reports of further clashes.
The raid was led by Puruji Indama, the Abu Sayyaf commander who was responsible for the kidnapping of two Chinese nationals and a Filipino worker in November.
Michael Tan and Oscar Lu were freed on Friday after being held hostage for more than three months.
Mark Singson, a Filipino national, who was captured with them, was later killed.
The Abu Sayyaf is a self-styled group of Muslim fighters blamed for the Philippines's worst attacks, including the bombing of a passenger ferry on Manila Bay that killed over 100 people in 2004.
Abu Sayyaf, which has about 400 fighters, has been blamed for numerous bombings, beheadings and kidnappings of Filipinos and foreigners, including Americans.
Several Filipinos have been kidnapped but most either escaped or were released, allegedly after ransom payments.
The military says fewer than 400 Abu Sayyaf members remain active in the islands of Basilan and Jolo, down from a peak of about 1,200 in 2002.
Abu Sayyah is believed to have received funds from al-Qaeda and is on a US list of "terrorist" organisations.