Several thousand Hong Kong school teachers and supporters braved thunderstorms to start a weekend of anti-government protests.

Demonstrators say they are fighting the erosion of the "one country, two systems" arrangement that enshrined some autonomy for Hong Kong since China took it back from Britain in 1997.

During the past week they have increasingly directed their frustrations toward police, who have responded with fiercer determination to clear them from the streets.

The teachers rally - which organisers estimated drew 22,000 people whereas police said 8,300 - had been approved by police.

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After gathering peacefully in the Central business district, they marched on the Government House residence of Hong Kong's embattled leader Carrie Lam, chanting "Hong Kong police know the law, they break the law".

"If Carrie bothered to respond to our demands at the very beginning, nobody would get hurt," a retired primary schoolteacher said.

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Anti-government demonstrators were also expected to march through Kowloon districts popular with traders and tourists from mainland China.

The pro-democracy Civil Human Rights Front, which organized peaceful marches in June, has scheduled another protest for tomorrow.

"We all feel tensions are building and the level of stress is increasing," one protester told Reuters during a sit-in at the international airport earlier in the week.

"I know violence cannot fight violence but sometimes aggression is needed to attract the attention of the government and others," he said.

"I have thrown rocks...I have also been hit by police with batons. We're all slowly getting used to this" the 22-year-old added.

Thousands of mostly young protesters forced a shutdown of flights at the city's Chek Lap Kok international airport on Monday, disrupting flights until late Tuesday.

The unrest presents one of the biggest challenges for Chinese President Xi Jinping since he came to power in 2012.

Western governments, including the United States, have stepped up calls for restraint following ugly and chaotic scenes at the airport.

Chinese officials have likened some actions by protesters to "terrorism" and Chinese state media outlets have urged tougher response from Hong Kong police.

Across the border, in the mainland city of Shenzhen, China's People's Armed Police units have staged extensive drills in recent days, but Hong Kong police say they can handle the situation.

Police have made some 750 arrests since the unrest began in June, and have charged some protesters with rioting which can attract a 10-year jail term as punishment.