Police killed at least 13 people in the Philippines capital, Manila, on the third night of an escalation in President Rodrigo Duterte's ruthless war on drugs, taking the death toll for one of the bloodiest weeks so far to 80.

Earlier this week, 67 people were shot and more than 200 arrested in Manila and provinces adjoining the city in what police described as a "one-time, big-time" push to curb the narcotics trade and street crime.

The term has been used by Philippine police to describe a coordinated anti-crime drive in crime-prone districts, usually slums or low-income neighbourhoods.

The spike in killings drew condemnation from Vice President Leni Robredo, who belongs to a party opposed to Duterte.

Branding it "something to be outraged about", she has been a constant critic of the crackdown that has killed thousands of Filipinos and caused international alarm since Duterte took office more than a year ago.

A team of Reuters journalists went to five communities in Manila on Thursday night where four men died in shootouts with undercover police in drug "buy-bust" or sting operations.

Police prevented the journalists from getting near the scene in the northwestern neighbourhood of Caloocan, but they saw three body bags being taken from a maze of narrow alleys. Elsewhere in Caloocan, they saw the corpse of a man slumped on an iron fence at the back of a mini-bus terminal.

Another man was killed near the Manila post office building, four died in hospitals in the northern area of Malabon, and another died on the spot near a former rubbish dump in the sprawling Quezon City district.

Three others were killed elsewhere on Thursday night, according to a radio report, including a man who was shot by masked men on a motorcycle in the eastern area of Marikina City.

Call for protest

"The killing spree must stop even as we also demand a stop to the proliferation of illegal drugs," Renato Reyes, secretary-general of the left-wing Bayan (Nation) movement, said.

"A long-term and thorough solution is necessary. A fascist solution is doomed to fail."

Reyes urged Filipinos to join a protest organised by a group of artists in Quezon City, saying in a flyer on social media: "Let us condemn the recent spike in the killings under the Duterte regime."

Police say there has been no instruction from higher authorities to step up their anti-drug operations and they are only doing their job.

"The president did not instruct me to kill and kill," national Police Chief Ronald dela Rosa said on Thursday. "I also don't have any instructions to my men to kill and kill. But the instruction coming from the president is very clear that our war on drugs is unrelenting. Those who were killed fought back."

READ MORE: Philippines' Duterte vows to continue his drug war

Duterte indicated this week that the escalation had his blessing, saying it was good that 32 criminals had been killed in a province north of Manila and adding: "Let's kill another 32 every day. Maybe we can reduce what ails this country."

On Thursday, he said he would not just pardon police officers who killed drug offenders during the anti-narcotics campaign, but also promote them.

Critics maintain that members of the Philippine National Police (PNP) are executing suspects and say it is likely they have a hand in thousands of unsolved murders of drug users by mysterious vigilantes. The PNP and government reject that.

Although the violence has been criticised by much of the international community, Filipinos largely support the campaign and domestic opposition to it has been muted.