Hong Kong protesters lit a fire outside court buildings, threw petrol bombs and spray-painted graffiti on government buildings, marring what was otherwise a "generally peaceful" march at the weekend, police say.
The comments came as protesters called for strikes across the city on Monday. Most railway and transport links ran smoothly during the morning rush hour and there were no reports of widespread disruptions.
Vast crowds of black-clad demonstrators had thronged the streets of the Asian financial hub on Sunday, in the largest anti-government rally since local elections last month and a resounding show of continued support for the pro-democracy movement.
While the march appeared to be largely peaceful - in marked contrast with some other mass demonstrations during the past six months, where protesters fought pitched battles with police - authorities said there was some damage after it ended.
"Some rioters spray-painted the exterior walls of the High Court, threw petrol bombs and set fire outside the High Court and the Court of Final Appeal, damaging government properties and seriously challenging the spirit of the rule of law," police said on Monday, adding shops and banks were vandalised in the Causeway Bay and Wan Chai areas of Hong Kong island.
The Hong Kong Bar Association condemned what it called "acts of arson and vandalism" and said those responsible must be brought to justice.
Protesters estimated the turnout at 800,000, while police said it was 183,000.
Police said they arrested 42 people at the weekend for rioting, possessing weapons and other charges. Police have arrested 6022 people in relation to the unrest since early June.
In an editorial, the official China Daily newspaper called on the Hong Kong government to uphold the rule of law.
"Many residents in Hong Kong are fed up with the violence and disruption that have plagued the city for months," said the newspaper, often used by Beijing to put out its message.
Hong Kong's new police commissioner had said he would take a "hard and soft approach" to the demonstrations, where acts of violence would be treated harshly but other issues more flexibly.
The chairman and president of the American Chamber of Commerce (AmCham) in Hong Kong were denied entry at the weekend to the neighbouring Chinese territory of Macau, without explanation.
AmCham chairman Robert Grieves and president Tara Joseph had been travelling to Macau for an annual ball.
The pair were told to sign a statement saying they "voluntarily agreed not to pursue entry to Macau".
Macau's security chief, Wong Sio Chak, declined to comment specifically on their cases and said it was speculation their refusal was linked to Beijing's response to US legislation backing pro-democracy protesters in Hong Kong, RTHK said.
The unrest in Hong Kong people started in June as demonstrations against a now-withdrawn bill allowing extradition to mainland China.
It has since morphed into calls for greater democratic freedoms and sometimes violent protests.
China has repeatedly blamed foreign powers, including the United States, for stirring up the unrest.
Australian Associated Press