Dolorfino did not say who the assailants might have been attempting to abduct.
At least six people were killed in the first explosion near a sports field, while the second explosion wounded 13 civlians near a Roman Catholic cathedral before a third bomb, placed near a mini-bus terminal, was detonated by soldiers.
Dolorfino said that the dead included at least three marines and three militants, including an Abu Sayyaf commander identified as Bensar Indama.
Major-General Juancho Sabban, the local Marine commander, said that the target of the attacks was unclear.
"The reports are still very sketchy," he said.
"I don't know the specific targets but definitely, these attacks fall under terrorism - that is to create chaos.
"Our Marines are now in control. The operations are still ongoing. They have cordoned off the city and we're asking the people to remain calm."
Rear Admiral Alex Pama, who heads a counterterrorism force, said the Abu Sayyaf fighters may have intended to detonate additional bombs and apparently tried to take hostages as they split into three groups and fled.
"They had a big plan, a major attack that we foiled," he said.
Isabela is one of two Christian regions on predominantly Muslim Basilan island, which has seen frequent clashes between Abu Sayyaf and government forces.
Abu Sayyaf, which is estimated to have nearly 400 fighters, says it is fighting for a separate Muslim homeland in the south of the Philippines.