Protesters smashed windows in a subway station and a shopping mall on Sunday as violence broke out across the New Territories of Hong Kong amid anger over a demonstrator's death and the arrest of pro-democracy politicians.

Key points: This is the 24th-straight weekend of anti-government protests in Hong Kong

This is the 24th-straight weekend of anti-government protests in Hong Kong Protesters are furious over what they say is police brutality

Protesters are furious over what they say is police brutality There are fears China will postpone or cancel upcoming district council election

Police made arrests and fired tear gas to break up rallies as black-clad activists blocked roads and trashed shopping malls across Hong Kong on the 24th-straight weekend of anti-government protests.

Protesters vandalised a train station in the central new town of Sha Tin and smashed up a restaurant perceived as being pro-Beijing, just two weeks before planned district council elections, the lowest tier of voting in the Chinese-ruled city.

Now TV showed pictures of a huge red welt on the upper arm of one of its reporters, who said she had been hit by a tear gas canister in Tsuen Wan, to the west of the New Territories.

A protester kicks away a police teargas shell as they clash outside a shopping mall in Hong Kong on Sunday. ( AP: Kin Cheung )

The rail station was closed in Sha Tin amid scuffles between police and protesters young and old, on a day of planned shopping mall protests throughout the territory. Shopping districts across the harbour on the main island were quiet.

"Radical protesters have been gathering in multiple locations across the territories," police said in a statement.

"They have been loitering in several malls and vandalising shops and facilities therein, neglecting the safety of members of the public."

Protesters daubed graffiti on shopfronts in Kowloon Tong and "stormed" shops in Tsuen Wan, police said.

Last weekend, anti-government protesters crowded into a shopping mall when a man slashed people with a knife and bit off part of a politician's ear.

Hong Kong is in the sixth month of protests that began in June over a proposed extradition law and have expanded to include demands for greater democracy and other grievances.

The protesters are furious at what they see as police brutality and meddling by Beijing in the former British colony's freedoms, guaranteed by the "one country, two systems" formula in place since it returned to Chinese rule in 1997.

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

They are 'escalating the anger of Hong Kong people'

Thousands of people gathered on Saturday night at a vigil for "martyrs", after a student died in hospital this week following a high fall.

Thousands attended a vigil for "martyrs" including Chow Tsz-Lok, who died after a high fall. ( AP: Kin Cheung )

Though the vigil ended peacefully, many attendees called for revenge after the student's death from injuries sustained during a protest.

Seven pro-democracy city politicians have been detained or face arrest and are due to appear in court on Monday on charges of obstructing a May meeting of the local assembly, police and several of the politicians said.

"We believe that the government together with the police, as well as the pro-establishment camp, they are trying to escalate the anger of Hong Kong people in order to cancel or even to postpone the upcoming district council election," Tanya Chan, a pro-democracy politicians, told reporters on Saturday.

One of the arrested politicians, Gary Fan, said the detentions were the result of "political prosecutions and judicial crackdowns" by Hong Kong chief executive Carrie Lam.

The elections are due on November 24.

Protesters have also called for a general strike on Monday and for people to block public transport, although such calls in the past have often come to nothing.

Protesters have thrown petrol bombs and rocks at police who have responded with tear gas, pepper spray, water cannon, rubber bullets and several rounds of live ammunition. They deny using excessive force.

Reuters/AP