Hong Kong leader Carrie Lam said Tuesday she has never tendered her resignation to China over the anti-government protests that have roiled the city for three months.

Lam was asked repeatedly at a news briefing about a Reuters report on Monday citing leaked audio of her telling business leaders recently that she would quit if she had a choice.

"I have never tendered a resignation to the central people's government. I have not even contemplated to discuss a resignation ... the choice of not resigning was my own choice," Lam said when asked why Beijing refused to let her quit.

"I know it is not going to be an easy path, and that's why I have said that I have not given myself the choice to take an easier path and that is to leave."

Lam also slammed the recording and leaking of her comments from the private meeting as "unacceptable."

Lam was elected as Hong Kong's chief executive by a pro-Beijing committee of Hong Kong elites, and the mainland government has spoken in support of her government and the city's police force throughout the sometimes-violent protests.

The demonstrators who have filled parks and streets regularly since early June want democratic reforms to Hong Kong's government and an independent inquiry into police actions against protesters.

Lam has come under withering criticism for pushing an extradition bill that would allow Hong Kong residents to be sent to mainland China for trials. She has suspended the bill, but the protesters want it entirely withdrawn.

Clashes between police and protesters have become increasingly violent, with demonstrators throwing gasoline bombs and rods at officers in protests last weekend. Authorities in turn have employed water cannons, tear gas, rubber bullets and batons. More than 1,100 people have been detained.

Lam said Tuesday that the "one country, two systems" formula under which the former British colony was returned to China in 1997 would be upheld. The formula promised greater civil rights in Hong Kong than those afforded to mainland Chinese, but Hong Kong residents have expressed worries that promise is eroding.

She also said the Chinese government believes that the Hong Kong government can overcome the conflict on its own, without any interference. Some have expressed fear the Chinese military would crack down on the protests.

Lam said she doesn't know how long it will take to end the civil disobedience but that she remains confident of restoring law and order.

The mostly young protesters say that a degree of violence is necessary to get the government's attention after peaceful rallies were futile. Lam's administration says the violence must end before any dialogue can begin.

In Beijing, the mainland office responsible for Hong Kong slammed the escalating violence and warned that China will "not sit idly by" if the situation worsens.

Yang Guang, spokesman for the Hong Kong and Macao Affairs Office of the State Council, told a news conference there were elements of "terrorism" and "clear features of a colour revolution" among the radical "separatists" in Hong Kong.

He distinguished the "thugs and rioters" from the large number of people who participated in peaceful demonstrations, saying their motive now is to paralyze the Hong Kong government and end the "one country, two systems" policy.

A spokeswoman, Xu Luying, said Beijing supports Lam's government in "using all necessary laws," when asked about the possible imposition of colonial-era emergency laws that provide greater power to detain people, impose curfews and censor the media.

She said Hong Kong's government can request help from the Chinese garrison to end the worst crisis since the city returned to Chinese rule, and that this would not mean the end of Hong Kong's autonomy as the deployment is provided for under current laws.

Xu also raised the possibility of invoking Article 18 of the Basic Law, Hong Kong's constitution, which stipulates that the National People's Congress can decide that a region is in a state of emergency that's beyond the control of the region's government, which effectively means that Beijing can intervene without Hong Kong's request.

"If the situation continues to deteriorate and morphs into a turmoil that endangers national sovereignty and security, the central government will never sit idly by," she said.

Tens of thousands of students clad in gas masks and hard helmets along with their formal school uniforms, boycotted the first day of classes Monday as part of a citywide strike. Workers also participated in a rally at a public park adjacent to the government headquarters.

The prolonged protests have hurt Hong Kong's economy amid a slowdown in the Chinese economy and its trade war with the United States.

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Associated Press writers Yanan Wang in Beijing and Eileen Ng in Kuala Lumpur, Malaysia, contributed to this report