Alexander Pama, a Philippine navy commander, said the gunmen ransacked the activist’s home before dawn on Friday before dragging him out.
“They fled on foot towards the interior of the island,” he said.
The Filipino caretaker of the house, who was shot at, managed to escape unharmed.
Al-Rasheed Sakalahul, the provincial vice-governor, said the caretaker was guiding the Philippine military in combing the nearby jungle to try to locate the hostage.
Police say Jalil is thought to have been taken by members of the Abu Sayyaf, a group of fighters that Philippine and Western intelligence agencies have linked to al-Qaeda.
Last month suspected Abu Sayyaf fighters kidnapped three Red Cross workers including two Europeans.
They are currently being held hostage on the island of Jolo, near to Basilan.
The Abu Sayyaf, notorious for ransom kidnappings and a string of high-profile attacks, is also holding captive three teachers, a nine-year-old boy and an employee of a Basilan money lending company.