Two people are in a critical condition in Hong Kong after another day of protests and violent clashes between anti-government protesters and police that left more than 60 people injured.

A police officer shot an unarmed 21-year-old male university student in the stomach as demonstrators attempted to disrupt the Monday morning rush hour as part of a day of planned protests and strikes.

Later in the day, a middle-aged man was doused in a flammable liquid and set on fire after arguing with protesters. Both the student and the man were in critical condition, according to Hong Kong’s Hospital Authority.

The two incidents, both captured on video, come after the death of a protester on Friday who succumbed to injuries sustained after falling from a car park during a police dispersal of demonstrators. It was the first death directly linked to police action.

The shooting and the man being set on fire, following closely after the death, could mark a turning point in five months of protests, which have grown increasingly violent.

Speaking to reporters, Hong Kong’s chief executive, Carrie Lam, said: “I do not want to go into details, but I just want to make it very clear that we will spare no effort in finding ways and means that could end the violence in Hong Kong as soon as possible.”

“If there is still any wishful thinking that by escalating violence the government will yield to pressure … I am making this clear and loud here. That will not happen.”

Monday’s incident is the third time police have shot demonstrators with live rounds. In the two previous cases, officers claimed they fired in self defence and the demonstrators, both teenagers, recovered. Some demonstrators have also grown increasingly violent, mobbing and beating critics and others they believe to be mainland spies.

The shooting, captured by local media Cupid Producer, showed a police officer struggling to subdue a protester firing three live rounds at nearby demonstrators. One protester, shot at close range in the torso, fell to the ground and was seen lying in a pool of blood. He appeared to be conscious and later attempted to run from police but was quickly caught.

The police said the officer had shot the demonstrator to prevent him from grabbing his revolver. “When a police officer uses force he has to consider the consequences. Remember, the police force faces a lot of life-threatening situations … A police officer has to protect himself,” a spokesman said, stressing that all officers must justify any use of force.

Footage of the man who was set on fire emerged in the afternoon, as protesters in various locations lit fires, vandalised public transit stations and traffic lights, and hurled petrol bombs at police. Confrontations between protesters and police continued into the night.

Video showed a man yelling “You are not Chinese!” at a group of young people on an overpass in Ma On Shan in Hong Kong’s New Territories. Someone appears to lunge forward, pouring liquid over the man before setting him alight.

Demonstrators on Monday also faced off with riot police outside of universities, seen as havens by protesters, many of them students. Demonstrators at Polytechnic University threw petrol bombs at police and set a barricade made out of ladders and noticeboards on fire in a huge blaze later put out by firefighters. At least six universities cancelled classes on Tuesday over “escalating tension and unrest”.

Police said protesters had earlier blocked the Cross Harbour tunnel, linking Kowloon to Hung Hom. Several mass transit railway (MTR) lines were delayed or suspended as some protesters smashed gates at stations. The MTR said a protester had thrown two petrol bombs into a carriage carrying commuters.

Police fired teargas and pepper spray and aimed their firearms at residents and demonstrators in multiple locations, including Hong Kong’s central business district. More than 260 people were arrested, according to the police.

In one incident, a police officer on a motorbike drove weaved in and out of a crowd of protesters on a road before hitting one, dragging the demonstrator along the road. The police said the officer had been suspended and the incident would be investigated.

“Hong Kong police gone nuts,” the pro-democracy lawmaker Claudia Mo tweeted alongside a video of the scene. “They seem to truly think they’re above the law. This has been almost like Tiananmen Square in slow motion.”

In Sai Wan Ho, a woman rushed at the police after the shooting and was subdued as residents called the officers “murderers”. Some threw plastic crates at the police, who pepper-sprayed the crowd.

Hong Kong faces its most serious political crisis in decades as protests, which began in response to an extradition bill that would send suspects to mainland China, have taken on new demands, chief among them an independent investigation into alleged police brutality.

The Hong Kong government has repeatedly said that an inquiry by Hong Kong’s police watchdog, the Independent Police Complaints Council, would suffice. But last week, a panel of experts appointed to advise the council said the watchdog lacked the authority and resources to effectively conduct an investigation.

The protests also pose a direct challenge to the “one country, two systems” framework under which Beijing maintains control over Hong Kong. Demonstrators are demanding the right to elect their own leader without interference from Beijing.

China has shown no sign it is willing to concede. Zhang Xiaoming, China’s top official overseeing Hong Kong affairs, said on Saturday that Beijing would ensure only those loyal to the central government would serve as leader.

“With both sides digging in, the conflict is likely to escalate,” said Ho-Fung Hung, a professor in political economy at Johns Hopkins University.

“With this televised shooting of an unarmed protesters point blank … the militant protesters would believe more firmly they have to fight back by any means necessary, and the public opinion will be further against the police and the government,” he said. “A war has started.”