Some sites have been unavailable for several hours, The Philippine Star reported. The targets included the sites of the National Bureau of Investigation and both houses of Congress.
Justice Secretary Leila De Lima ordered the hackers' arrest based on new laws.
"They will trace who the hackers are and apprehend them. For this purpose, they need to coordinate with the intelligence units of other investigative bodies," De Lima said.
The hackers face six to 12 years in prison if they are convicted. But Radio Australia reported they appear to be based in Europe.
De Lima said the new laws have a legitimate purpose: "The purpose of the law is to protect our citizens from unscrupulous and abusive actions of misfits and the wicked in society."