At least five people, including Parojinog's daughter, who serves as vice mayor of Ozamiz, a port city, were arrested during the raids.
"The administration vowed to intensify the drug campaign", Abella said. Several others, including Mr Parojinog's wife, were killed during the raid.
Police said they had conducted surveillance on Parojinog based on the president's remarks.
Parojinog, who also faced corruption charges, had denied any links to illegal drugs.
'The Parojinogs, if you would recall, are included in President Duterte's list of personalities involved in the illegal drug trade, ' Ernesto Abella, the president's spokesperson, said in a statement.
Among those Mr. Duterte named was Reynaldo O. Parojinog, Sr., mayor of Ozamiz City, Misamis Occidental.
The grenade explosion, he said, was possibly hurled by cops to scare away the people who were allegedly trying to prevent the cops from planting evidence.
Espino added that the police in the region will not have second thoughts in arresting and going against government officials who are into the illegal drugs trade, especially that "we have the full support of President Rodrigo Duterte".
She also said that she's in fear for her life.
In October Samsudin Dimaukom, the mayor of the southern town of Saudi Ampatuan, was killed in a shoot-out at a police checkpoint on suspicion he and his security personnel were transporting illegal drugs, authorities said.
Meanwhile, Espino said with Parojinog's death, Central Visayas will now be safe from the criminal group known as Ozamiz Kuratong Baleleng.
Senior Supt. Jaysen de Guzman, police chief for Misamis Occidental, said a total of 13 people were killed, including the mayor.
Pacleb said Parojinog's involvement in illegal drugs and his bodyguard's use of unlicensed firearms prompted the implementation of the search warrant.
Mayor Reynaldo Parojinig, his wife Susan Parojinig, brother Board Member Octavio Parojinig Jr., Camerman JR Millanar of Lumad TV and the Ozamiz Information center, Mona Parojinig, Miguel Del Victoria, Nestor Cabalan, Daniel Vasquez, "Inting", and four other unidentified people were killed in raids in barangays Baybay San Roque and Baybay Santa Cruz around 2:30 a.m., Ozamiz City stringer Thata Roxas from the Mindanaoan Broadcasting Channel told CNN Philippines. Duterte said past year that the majority of drug transactions happen inside the prison.
He is the third mayor to have been killed in President Rodrigo Duterte's crackdown on narcotics.
The family was also tagged as the founder of Kuratong Baleleng, a gang of former military men who were into kidnapping and bank robberies in the 1980s.
Espenido was the Albuera police chief when the then-detained Espinosa was killed during a police raid in a jail in a nearby city in Leyte. Marcos claimed they were forced to retaliate and shoot them to death when they resisted while they tried serving an arrest warrant against them.