Video footage showed an officer drawing a pistol with one hand while holding a protester with the other. As another protester, who friends say was Mr. Chow, approached the officer and reached toward the pistol, the officer fired three times, striking Mr. Chow once in the stomach. Police said the officer acted in self-defense to stop the protester from grabbing his gun.

Trust in Hong Kong’s police force has plunged since police first used tear gas against protesters in June, polls show, and officers now routinely use tear gas, rubber bullets, batons and water-cannon blasts while trying to disperse and arrest protesters. Police tactics have shifted as some protesters have become more radical and confrontational, with black-clad youths flinging Molotov cocktails and bricks and at times attacking people suspected of sympathizing with Beijing.

The police force has repeatedly said it uses the minimum force necessary to maintain order and has condemned what it sees as increasingly violent actions by protesters. On Monday, police officials showed footage of a 57-year-old man being set ablaze in an attack they blamed on protesters. The man, whom local media identified as Leung Chi-cheung, was reportedly in critical condition.

“If there is still any wishful thinking that by escalating violence the government will yield to pressure to satisfy the so-called political demands, I am making the statement clear and loud here, that will not happen,” Hong Kong’s leader, Chief Executive Carrie Lam, said Monday.

Mrs. Lam reiterated that a probe by the existing Independent Police Complaints Council must run its course before any other investigations can be considered. The council is due to issue an initial report in the next few weeks.

Participants in the protest movement have demanded a judge-led independent investigation into allegations of excessive force and brutality. Critics said the council lacks resources and powers such as summoning witnesses. Those concerns were shared in recent days by an international panel of experts called in by the government to advise the council on its investigation.

In a tweet on Saturday, Clifford Stott, one of the experts and a social-psychology professor researching public-order policing at Britain’s Keele University, shared a statement from the panel that called into question the council’s ability to conduct independent investigations into policing practices, given the scale of events in Hong Kong and the council’s restrictions on collecting and validating evidence.

With the government refusing to establish an independent inquiry, public anger has risen as police have drawn weapons during skirmishes with demonstrators, shooting three protesters in recent weeks. Tensions rose in recent days after a university student died of injuries sustained during a fall at a parking garage while officers nearby were dispersing protesters. 

Anger was visible Monday at a dense community of apartment towers near the parking garage, which has become a makeshift memorial for the student. On Monday morning, dozens of young protesters milled around outside the parking garage with bricks in their hands, expecting police to show up. Others gathered inside around the memorial.

“We think the police just want to kill us all,” said an 18-year-old university student standing over the shrine. When police arrived outside, she pulled on a black sweatshirt and ran toward the developing front line.

Police fired tear gas in several directions, including into the garage. Protesters scattered into apartment towers. The tear gas wafted into residences, a primary school and secondary school, and a shopping arcade.

Local residents poured into the streets. Police attempted to enter the courtyards of apartments where protesters had fled, but were shouted back by the crowd. Outnumbered, the police retreated, sometimes leveling shotguns at the crowd.

Hong Kong’s police force was previously largely respected by citizens. But the force had limited exposure to dealing with violent disruptions until this summer and has been stretched thin from monthslong protests that take place several times a week.

Recent polls show that the police have lost the support of the majority of people in Hong Kong. An October survey by the Chinese University of Hong Kong showed more than half of the 751 people interviewed had zero trust in the city’s police force, a sharp rise from 6.5% at the start of the summer.

Amnesty International called for an investigation into the police’s actions on Monday. “These are not policing measures—these are officers out of control with a mind-set of retaliation,” said Man-Kei Tam, director of Amnesty International Hong Kong.

The Hong Kong police spokesman dismissed the claim. “We are under great pressure. Our officers also encountered difficult times during the operations,” he said, adding that police have guidelines to use force as responsive measures.

More than 250 officers have been injured since June, police said in late September.

Regina Ip, a pro-Beijing lawmaker and adviser to Mrs. Lam, said the priority of the Hong Kong police must be to quash unrest and restore order. “Police are not there to win a popularity contest. Their job is to enforce the law and maintain order,” she said.

Police officials have repeatedly pushed back against public criticism and blamed protesters for escalating violence.Earlier this month, the chairman of the Junior Police Officers’ Association, Lam Chi-wai, wrote an open letter to the group’s 25,000 members condemning what he called “crazed targeted attacks” and “smears” against the police. He praised fellow officers for “overcoming countless difficulties and performing duties professionally and in accordance with the law.”

Those views were hard to come across at lunchtime on Monday in the Central district, an area crammed with offices and luxury retail stores. Outrage subsumed hunger for some office workers who streamed onto the streets to denounce what they called police violence.

Hundreds of people in office attire—from shirts and blouses to suits—lined up alongside black-clad youth to shout abuse at police officers in riot gear. Nearby stores shut down early, while traffic ground to a halt as protesters build barricades to block key roads.

Police fired tear gas down a street, sending protesters and passersby scurrying to escape the choking fumes.

The crowd roared with antipolice invective. “Black police, may your entire families die,” one chant went. “Hong Kong people, seek revenge,” went another. Others demanded the disbandment of the police force.

A 38-year-old entrepreneur, who gave his surname as Cheung, said he joined the protest after seeing television reports about the shooting while working at his office in Central. “The police are abusing their power,” he said. “This shouldn’t be happening in a civilized city.”

—Rachel Yeo, Jing Yang, Joanne Chiu and Natasha Khan contributed to this article.

Write to Eun-Young Jeong at Eun-Young.Jeong@wsj.com, John Lyons at john.lyons@wsj.com and Chun Han Wong at chunhan.wong@wsj.com