Hong Kong's embattled leader insisted Tuesday she had no intention of stepping down, after an audio recording emerged of her saying she wanted to quit and apologise for causing the unrest that has rocked the southern Chinese city.

Hong Kong has endured three months of violent pro-democracy protests, triggered by opposition to Chief Executive Carrie Lam's bid to push through a law allowing extraditions to mainland China.

The protests evolved into a wider democracy campaign involving violent clashes between protesters and police, in the biggest challenge to China's rule of Hong Kong since its 1997 handover from the British.

"I told myself repeatedly in the last three months that I and my team should stay on to help Hong Kong," Lam told a press conference on Tuesday morning.

Lam said she had "not even contemplated" discussing resigning with the Chinese government, which gives Hong Kong a restricted form of autonomy but ultimately is in charge of the territory.

Lam was speaking after the Reuters news agency released an audio recording of her telling business leaders last week she wanted to step down and take responsibility for the unrest.

"For a chief executive to have caused this huge havoc to Hong Kong is unforgivable," Lam said in the audio recording.

"If I have a choice," she said, speaking in English, "the first thing is to quit, having made a deep apology."

Lam told the business leaders she had "very limited" room to resolve the crisis because it had become a national security and sovereignty issue for Beijing.

Lam described the leaking of the audio recording as "quite unacceptable", and denied accusations that she or her government had orchestrated it.

"The conflict that I myself want to quit but cannot quit does not exist," she said.

Rallies over the weekend saw some of the worst violence of the crisis, with protesters throwing bricks and petrol bombs at police, who responded with tear gas, water cannon and baton charges.

More than 1,100 people have been arrested since June when the unrest began, including a swoop of key pro-democracy leaders and politicians late last week.

China has responded to the crisis by ramping up threats and intimidation, including by warning its security forces could intervene.

Chinese state media have released videos showing mainland security forces deployed just across the border.

An editorial by China's state news agency on Sunday warned the protesters that "the end is coming".