The accusations by the National Bureau of Investigation deepened concerns that police were carrying out summary executions as part of Duterte's controversial war on crime, which has claimed more than 5,100 lives in just over five months.
The NBI, equivalent to the Federal Bureau of Investigation in the United States, said police shot dead mayor Rolando Espinosa and his cellmate Raul Yap, as they were defenceless in a provincial jail cell last month.
"Rub out" is a local expression, referring to the police killing a suspect and then saying he died in a gun battle.
"The pieces of evidence, both testimonial and the forensic evidence all agree. We believe we have a very strong case," NBI deputy director Ferdinand Lavin told reporters.
The accused police had claimed they fired in self defence at the pair when they went into the jail cell before dawn to execute a search warrant.
The police alleged Espinosa, who was in jail after being arrested in October on drug and gun possession charges, had a firearm and methamphetamines in the cell.
Lawmakers, media groups and human rights advocates had ridiculed that version of events, asking why police had to execute a search warrant in a jail cell at night and why CCTV footage of the event had disappeared.
Duterte's police chief stood down the police officer in charge pending an investigation, but the president immediately reinstalled him.
Duterte had accused Espinosa, mayor of Albuera town in the eastern province of Leyte, of being a drug lord.
In a speech late yesterday, the president again defended the police in the Espinosa case.
Duterte, 71, won May elections in a landslide on a promise to kill tens of thousands of criminals to prevent the Philippines from becoming a narco-state.
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