Reyes said it is a crime for anyone to take the life of another person, and the government and the public do not condone vigilantism.
"We don’t tolerate people, other than those duly designated and allowed by law to carry firearms and impose the law, to do it on their own initiative," Reyes told reporters.
"I have directed the police to continue to find out who are responsible for these killings. We have to identify the suspects," Reyes said.
He also said he is not giving the local police force an ultimatum, but that the order should be carried out as soon as possible.
The Cebu City chapter of the Integrated Bar of the Philippines had earlier sought the help of President Arroyo in stopping the series of vigilante-style killings here that have remained unsolved with no suspect charged.
The appeal of the Cebu City IBP chapter came after suspected vigilantes struck again last week, killing two persons — a rugby user and a suspected thief, bringing the number of victims of vigilante-style killing to at least 40 persons since December last year.
In a resolution, officers of the Cebu City IBP chapter urged President Arroyo to intercede and put an end to the unabated summary executions of suspected criminals in the city.
"Despite opposition by responsible quarters, such summary executions remain unsolved, leading to the prevailing belief that police and the local officials either encourage or tolerate illegal acts or remain indifferent, or have been remiss in their duties to enforce the law," the IBP resolution stated.
At least 40 suspected criminals have been killed in a summary-execution style that began on Dec. 23 last year, just two days after Mayor Tomas Osmeña announced he was creating a so-called Hunters Team to "seek and destroy" criminals and other notorious characters.
The killings have drawn the condemnation of some officials and leaders, including Cebu Archbishop Ricardo Cardinal Vidal and Vice Mayor Michael Rama.
Some concerned residents believed the gunmen were policemen because the series of killings took place after Osmeña announced that lawmen who could finish criminals off would be rewarded.
The police, however, denied involvement in the killings.