Carrie Lam herself insisted earlier on Tuesday she had no intention of stepping down

Beijing on Tuesday threw its backing behind Hong Kong leader Carrie Lam after an audio recording emerged of her saying she wanted to quit over three months of unrest in the semi-autonomous city.

"We firmly support Hong Kong chief executive Carrie Lam in leading the SAR (Special Administrative Region) government," Yang Guang, spokesman for the Hong Kong and Macao Affairs Office of China's central government, said at a press conference.

Hong Kong has endured dozens of sometimes violent pro-democracy protests triggered by opposition to Lam's bid to push through a law allowing extraditions to mainland China.

The demonstrations have evolved into a wider democracy campaign involving clashes between protesters and police, in the biggest challenge to China's rule over Hong Kong since the city's 1997 handover from the British.

The Chinese government expressed its support for Lam after Reuters news agency released an audio recording of her telling business leaders last week that she wanted to step down and take responsibility for the unrest.

Lam herself insisted earlier on Tuesday she had no intention of stepping down.

"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 in the city.

Lam said she had "not even contemplated" discussing her resignation with the Chinese government, which gives Hong Kong a restricted form of autonomy.