A protester was injured on Monday morning when he was shot at close range by a police officer.
He was the third person shot by police since the protests began 24 weeks ago.
Later on Monday a pro-Beijing supporter was doused in flammable liquid and set alight after arguing with protesters, who are demanding greater democracy and police accountability in Hong Kong.
The territory's Chief Executive Carrie Lam, speaking at a news conference on Monday evening, called the demonstrators enemies of the people.
"If there's still any wishful thinking that by escalating violence, the Hong Kong government will yield to pressure, to satisfy the so-called political demands, I'm making this statement clear and loud here: that will not happen," she said.
There were clashes across Hong Kong on Monday between protesters and police, who fired rubber bullets and tear gas. At one point, tear gas was fired in the central business district - a rare occurrence during working hours on a weekday.
The violence also prompted a warning from a senior Chinese newspaper editor at a tabloid published by the state-owned People's Daily.
Addressing Hong Kong police, Hu Xijin wrote: "You have the backing of not only the Hong Kong and Chinese people, but also Chinese soldiers and the People's Liberation Army in Hong Kong," Reuters news agency reported. "They can go into Hong Kong to provide support at any time."
Monday's violence followed a weekend of vigils and protests after a 22-year-old student protester died on Friday. Alex Chow had been in hospital since he fell from the ledge of a car park during a police operation a week ago.
The protests started in June against a now-withdrawn plan to allow extradition to mainland China, but have since morphed into wider demonstrations.