Hong Kong Chief Executive Carrie Lam says her administration will "spare no effort'' to end the anti-government protests that have wrecked the city and brought it "to the brink of no return" for more than five months.

"My friends, including some senior citizens, messaged me asking if it is safe to go out. We are questioning if we can live in this city safely," Lam said.

Lam said in a defiant televised press conference on Monday that she did not want to go into details, but her comments were likely to fuel speculation that harsher legal and police measures might be in the works.

She strongly stated her support of the Hong Kong police, and said that there would be no giving way to protesters' demands for political concessions.

In a statement, the Hong Kong government said police had been responding to vandalism and disruptions of traffic, including protesters throwing heavy objects onto roads from above.

"During police operations, one police officer has discharged his service revolver, one male was shot,'' the statement said, adding that officers also drew their guns in the Shatin and Tung Chung neighbourhoods.

The statement denied what it called online rumours that police had been ordered to "recklessly use their firearms,'' calling the allegation "totally false and malicious.''

"These rioters' actions have far exceeded their demands, and they are enemies of the people,'' Lam said.

"If there is still any wishful thinking that, by escalating violence, the Hong Kong SAR government will yield to pressure to satisfy the so-called political demands, I am making this statement clear and loud here: That will not happen,'' Lam said, using the initials for Special Administrative Region, which describes the city's status as a semi-autonomous Chinese territory.

Lam's clear message comes on a day of violent protests around the city, which escalated after police shot a 21-year-old protester with a live round. The protester is currently in hospital in critical condition.

It was the second protester shot since the demonstrations began in early June, although police have repeatedly drawn their firearms to ward off attacks.

Police said they arrested more than 260 people on Monday, adding to the more than 3,300 arrests since the movement erupted in June.

Police Spokesman Tse Chun-chung said the shooting, burning and motorcycle incidents were all under investigation, but defended the officers' actions as necessary for their own safety.

Tse said two people were arrested in the shooting incident, including the person shot, but no one has yet been detained over the burning.

Another person is in critical condition after protesters doused him in a flammable liquid and set him alight. Lam said the incident was "horrific."

"This is a blatant breach of peace and rule of law and totally inhumane act that nobody should condone," she added.

Lam said Monday’s "social disturbances" resulted in "a large number of casualties", as 60 people have been injured through the course of the day.

Protesters, who had already begun a city-wide day of action aimed at paralysing the international financial hub, reacted to the morning shooting by rampaging through train stations, barricading streets and vandalising shops.

Protesters built barricades and blocked roads at about 120 locations across the city of 7.4 million and demonstrations were still ongoing, the police spokesman added.

"Continuing this rampage is a lose-lose situation for Hong Kong. Everyone is a loser,'' he said.

The UK government sees the violence at pro-democracy protests in Hong Kong that saw a police officer shoot a masked demonstrator and a man set on fire as "deeply disturbing."

"Today's events are deeply disturbing. We are seriously concerned by the ongoing violence, and the escalation between protesters and police," said a Foreign Office spokesman.

UK Prime Minister Boris Johnson's Downing Street Office earlier urged for "calm and restraint on all sides", saying Johnson supported "the right to peaceful protects."

"Political dialogue is the only way forward and we want to see the HK authorities agree a path to resolve this situation," he added.

The protests began five months ago over a proposed extradition law and have expanded to include demands for greater democracy and police accountability as activists say that Hong Kong's autonomy and Western-style civil liberties, promised when the former British colony was returned to China in 1997, are eroding.

They are angry about meddling by Beijing in the freedoms guaranteed to the former British colony by the "one country, two systems" formula.

China denies interfering and has blamed Western countries for stirring up trouble.