A leaked audio recording has emerged in which Hong Kong’s leader, Carrie Lam, can be heard saying she would quit if she had “a choice” but suggesting she was being prevented from doing so by authorities in Beijing.

In the recording, obtained by Reuters, the Hong Kong chief executive told a group of businesspeople in a closed-door meeting last week she was “very, very limited” in how her government could respond to the mass protests that began in June over a proposal to allow extradition to mainland China.

“For a chief executive to have caused this huge havoc to Hong Kong is unforgivable. If I have a choice, the first thing [I would do] is to quit, having made a deep apology,” Lam said, her voice breaking with emotion. “So I make a plea to you for your forgiveness.”

The remarks further demonstrate that it is Beijing rather than Lam directing the government’s response to a political crisis that has threatened China’s authority over the city, as protesters continue to take to the streets pressing for the extradition bill to be withdrawn and calling for universal suffrage.

Clashes continued on Monday night when police fired teargas to clear protesters in Mong Kok, a commercial and residential area in Kowloon.

Play Video 0:53 Thousands of Hong Kong students boycott first day of term - video

In the leaked recording, Lam said she was constrained by the fact the situation had reached “a sort of sovereignty and security level” of concern to the Beijing leadership, especially in the midst of “unprecedented tension between the two big economies of the world” – a reference to deteriorating economic and diplomatic ties between the US and China.

“The political room for the chief executive who, unfortunately, has to serve two masters by constitution – that is, the central people’s government and the people of Hong Kong – that political room for manoeuvring is very, very, very limited,” she said.

As police appear to be cracking down more severely on protesters, resulting in more violent clashes, observers have wondered whether Hong Kong authorities have been ordered to put down the protests before 1 October, when the People’s Republic of China marks its 70th birthday, a national holiday that Beijing would not want to see tarnished.

But Lam said Beijing had not imposed a deadline and was willing to wait out the unrest, even at the cost of damaging Hong Kong’s economy. Officials were making special arrangements for a “modest but solemn” 1 October celebration amid expectations of disruption.

“I can assure you that Beijing does not have a deadline. They know this will ripple on,” she said. “They are willing to play long, so you have no short-term solution. Hong Kong suffers, you lose tourism, economy, you lose your IPOs and so, but you can’t do much about it.”

Lam said there were no plans for China’s People’s Liberation Army (PLA) to be deployed. “My own feeling [of] the pulse and through discussions, [Beijing] has absolutely no plan to send in the PLA.”

Lam’s comments came to light on Monday as thousands of university and secondary students in Hong Kong boycotted the first day of the new term , instead holding rallies and facing off against riot police in skirmishes into the night.

Thousands of students wearing helmets, goggles and masks – the unofficial uniform of the protesters – filled the grounds of the Chinese University of Hong Kong (CUHK), holding black banners saying “Boycott for freedom” and periodically shouting “Reclaim Hong Kong”.

“If you are not a slave, don’t act like one,” said one speaker, a woman introduced only by her surname, Chiu, from an alumni group, who urged students to remember their rights. A stage behind her featured a saying by Mao Zedong: “A single spark can start a prairie fire.”

University students have called for a two-week boycott, while secondary students have vowed to protest for one day a week until demonstrators’ demands are met.

In a park across the city, outside of the government’s headquarters, thousands more gathered in solidarity with students for a workers’ rally. In the evening, dozens of protesters gathered outside the garrison for PLA troops stationed in the city.

“If we are stopped by their violence, if we are frightened, I think our whole future will be over. It will be one country, one system,” said Phillip Tsoi, 19, who was shining a laser into windows of the PLA complex to antagonise those inside.

Hong Kong, a former British colony under Chinese rule since 1997, is meant to enjoy certain freedoms and autonomy under a the “one country, two systems” framework, according to the terms of the handover.

Tensions between protesters, who say that promise has been broken, and authorities have escalated dramatically in recent weeks. On Saturday, police fired teargas and water cannons with dye at protesters who threw petrol bombs and lit fires. Police also targeted protesters and commuters in metro stations, beating them with batons. On Sunday, protesters paralysed transport links to Hong Kong airport.

On Monday, police said more than 1,000 people had been arrested since the demonstrations began in June, including 159 over the weekend, among them a 13-year-old boy found with two petrol bombs.

China’s foreign ministry spokesman, Geng Shuang, said in a regular news briefing on Monday that the demonstrations in Hong Kong had “completely exceeded the scope of freedom of assembly”. “They have evolved into extreme and violent actions,” he said, reiterating Beijing’s support for the Hong Kong government and police.

In an English-language editorial on Sunday, the Xinhua state news agency said: “The end is coming for those attempting to disrupt Hong Kong and antagonise China.”

Hong Kong residents say their city feels increasingly like it is under martial law. After the weekend of tense clashes, riot police patrolled railway stations as protesters blocked train doors from closing, causing delays and throwing morning rush hour into chaos. Police were seen arresting at least one group of protesters and searching people on the street.

On Monday morning, secondary school students kneeled, held hands and chanted in the rain outside their schools. A typhoon warning had closed many primary schools.