Hong Kong's leader has warned that police will take "all actions necessary" to ensure government offices and schools reopen on Monday.
CY Leung called on demonstrators to allow the government and citizens to "resume their normal work and life" after a week of disruption.
Activists oppose China's plans to vet candidates to replace Mr Leung in 2017 and are demanding fully free elections.
Tens of thousands remained on the streets on Saturday night.
Mr Leung's televised comments came after street fights led to the postponement of talks between the government and the protesters.
Thousands are attending an anti-violence demonstration in the Admiralty district, and the BBC's Babita Sharma in Hong Kong, says the protest is one of the largest yet.
However, there were sporadic clashes throughout the day in Mong Kok, an area that saw some of the worst violence on Friday night.
At the scene: John Sudworth, BBC News, Hong Kong
After a day or two of dwindling numbers, the huge crowds outside the Hong Kong government offices tonight suggest that this is not a protest movement ready to give in.
The violence of last night, when thugs thought to be connected to the city's criminal triad gangs attacked the students, has had the opposite effect to that intended - galvanising support not diminishing it.
The ultimatum to leave the streets by Monday, issued via television address by CY Leung, also seems to have fallen on deaf ears.
Two very different views of how politics and society should work are locked in opposition to each other. It is exhilarating but also troubling because the slim hope of compromise and face-saving evident earlier in the week has now evaporated.
Neither fear nor fatigue, let alone the futility of wresting more democracy from the hands of China's communist rulers, have dampened enthusiasm for this cause.
'Social order must resume'
Mr Leung said he "strongly condemned" the violence but warned that it was likely to continue unless "social order" resumed.
"The government and the police have the responsibility and resolution to take all actions necessary to resume social order and let the government and all seven million citizens resume their normal work and life," he said.
He said the "most urgent thing" was for protesters to allow government staff to return to work and to clear main roads so schools can reopen on Monday.
The BBC's John Sudworth in Hong Kong says that although he did not explicitly threaten to clear the streets by force, CY Leung's televised address sounded every bit like an ultimatum.
The Hong Kong Federation of Students withdrew from planned negotiations following several street fights on Friday, accusing the government of allowing gangs to attack protesters, a claim denied by Hong Kong's security chief, Lai Tung-kwok.
Police said they had arrested 19 people who had been involved in the fighting, adding that eight of them had "triad backgrounds".
Correspondents say triads have traditionally been known for drug-running, prostitution and extortion networks but have in recent years become involved in legitimate ventures like property development and finance.
Some are also believed to have links with the political establishment, fuelling accusations that they have been paid by the authorities to stir up trouble.
At the heart of the row between the protesters and the government is China's insistence on tight rules on nominations for candidates wanting to stand for election in 2017.
The protesters say the restrictions mean the polls will fall short of the free elections they are seeking and have called for Mr Leung to step down.
But the central government in Beijing has thrown its full support behind Mr Leung, calling the protests illegal and "doomed to fail".
Hong Kong democracy timeline
- 1997: UK gives Hong Kong back to China under a 1984 agreement giving it "a high degree of autonomy" for 50 years
- 2004: China says it must approve any changes to Hong Kong's election laws
- June-July 2014: Pro-democracy activists hold an unofficial referendum on political reform; both sides hold large rallies
- 31 August 2014: China says it will allow direct elections in 2017 but will pre-approve candidates
- 22 September 2014: Student groups launch a week-long boycott of classes
- 28 September 2014: Occupy Central and student protests join forces and take over central Hong Kong
- 2017: Direct elections for chief executive due to take place
- 2047: Expiry of current agreements
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