In a televised address, Mr. Duterte said it was vital everyone cooperates and follows home quarantine measures, as authorities try to slow the contagion and spare the country's fragile health system from being overwhelmed, Reuters reported.
The Philippines has recorded 96 coronavirus deaths and 2,311 confirmed cases, all but three in the past three weeks, with infections now being reported in the hundreds every day.
"It is getting worse. So once again I'm telling you the seriousness of the problem and that you must listen," Mr. Duterte said late on Wednesday.
"My orders to the police and military... if there is trouble and there's an occasion that they fight back and your lives are in danger, shoot them dead."
"Is that understood? Dead. Instead of causing trouble, I will bury you."
His comments came after media reports of a disturbance and several arrests on Wednesday of residents in a poor area of Manila who were protesting about sufficient government food aid.
They also follow outrage among the medical community about social stigma and instances of hospital workers suffering physical abuse and discrimination, which Mr. Duterte said must be stopped.
Activists deride Mr. Duterte over his fierce rhetoric and accuse him of inviting violence and vigilantism, as shown in his war on drugs, during which police and mystery gunmen have killed thousands of people accused of using or selling drugs.
Police say their actions in the anti-drug campaign have been lawful.
Mr. Duterte's office typically calls his remarks hyperbole to underline his point.
The national police chief on Thursday said police understood that Mr. Duterte was demonstrating his seriousness about public order, and no one would be shot.