Brutal attacks on election candidates in recent weeks have thrust the lowest tier of government in the Chinese-ruled city into the world spotlight as Lam struggles to quash angry demands for universal suffrage.

Government data showed more than 2.1 million people had voted by 4.30pm on Sunday, or a turnout rate of 52 per cent, with six hours left until polling stations closed, way above the 1.47 million who voted in the last district elections four years ago. Police presence was thin.

First results should start trickling in before midnight.

Jimmy Sham, a candidate for the Civil Human Rights Front, which organised some of the mass anti-government rallies of recent months, was beaten by men with hammers in October.

"We can see Hongkongers are longing for a chance to express their stand," he said.

"We don't know yet, at the end of the day, if the democrats can win a majority. But I hope our Hong Kong citizens can vote for the future of Hong Kong."

Beijing-backed Lam cast her ballot in front of television cameras and pledged that her government, widely seen as out of touch, would listen "more intensively" to the views of district councils.

"I hope this kind of stability and calm is not only for today's election, but to show that everyone does not want Hong Kong to fall into a chaotic situation again," Lam said.

The anti-China protests have at times forced the closure of government, businesses and schools in the city's worst political crisis in decades, as police used tear gas, rubber bullets and water cannon in response to petrol bombs, rocks and occasionally bows and arrows.

A record 1104 candidates were vying for 452 seats and a record 4.1 million people have enrolled to vote for district councillors who control some spending and decide issues such as recycling and public health.

If the pro-democracy campaigners gain control, they could secure six seats on Hong Kong's Legislative Council, or parliament, and 117 seats on the 1200-member panel that selects its chief executive.

The protests started over a now-withdrawn extradition bill that would have allowed people to be sent to mainland China for trial but rapidly evolved into calls for full democracy, posing the biggest popular challenge to Chinese President Xi Jinping since he came to power in 2012.

Sunday was the seventh day of a stand-off at Polytechnic University, its campus surrounded by police as some protesters hid out on the sprawling grounds.

Demonstrators are angry at what they see as Chinese meddling in the freedoms promised to the former British colony when it returned to Chinese rule in 1997. They say they are also responding to perceived police brutality.

China denies interfering and says it is committed to the "one country, two systems" formula for the autonomy of Hong Kong.

Australian Associated Press