China is facing tough choices over how to tackle months of pro-democracy protests in Hong Kong: hold dialogue with protesters, play the long game or send in troops.

The protesters have shown no sign of backing down despite increasingly violent confrontations in which Hong Kong's police have used water cannon, tear gas and rubber bullets -- and even fired live warning shots.

In a leaked audio recording this week, the semi-autonomous city's leader Carrie Lam apparently sought to reassure businesses that Beijing "has absolutely no plan to send in the PLA (People's Liberation Army)".

But hours later Beijing again sent mixed signals about how it might ultimately handle the crisis, saying it will "never sit idly by" if the situation further deteriorates.

The protests were first triggered by opposition to a planned law that would have allowed extraditions to mainland China, and then evolved into a wider movement for democratic reform.

Here are the potential strategies for Beijing as it seeks to end the crisis:

Beijing's current approach has been to express firm public support for the Hong Kong police and Lam, while warning the protesters their actions are "intolerable".

The party is also preparing for the 70th anniversary of the founding of Communist China on 1 October.

In the leaked recording obtained by Reuters news agency, Lam told business leaders that Beijing has not set a "deadline" to quell the protests before the celebration.

"They are willing to play long, so you have no short-term solution," Lam said.

Beijing took a wait-and-see approach during the 2014 pro-democracy "Umbrella Movement" in Hong Kong, which saw protesters occupy parts of the city for more than two months. Those protests faded away without winning concessions from China after key leaders were arrested.

With schools and universities starting term this week, Beijing has been hoping protests will die down as students return to class.

But a strategy of non-engagement could make President Xi Jinping's government, which has taken a firm line on dissent, appear weak.

Beijing could pressure Hong Kong's government into finding some way to compromise with the protesters.

In a press conference on Tuesday, a central government spokesman said there was a need to address problems in Hong Kong society including the income gap and property prices, appearing to strike a more conciliatory tone.

The government could also orchestrate Lam's resignation, a key demand of the protesters.

But this looks increasingly unlikely.

In the leaked audio recording, Lam said if she had "a choice" then she would want to step down, suggesting the central government wants her to remain in office for now.

And any conciliatory measures would be seen to be giving in to the protesters and rewarding their actions.

The central government could step up pressure and intimidation tactics.

Beijing has already said the protests are "terrorism emerging" while state media has warned "the end is coming".

Police admitted they have used undercover officers to pose as protesters, sowing fear and suspicion among demonstrators which helped fuel violent scenes at Hong Kong's airport, where two mainlanders were tied up and beaten.

A mob attack on protesters was carried out by suspected pro-Beijing triad gang members, and the central government has been cracking down on businesses perceived to be supporting the protests.

"(Beijing's approach) seems to involve a mix of an escalation in the use of force by the police, a surge in arrests of both frontline protesters and purely peaceful democracy activists, a push for ideological control over businesses, universities and other institutions and... accelerating the city's economic integration into mainland China," said Ben Bland, director of the Southeast Asia project at the Lowy Institute.

The riskiest strategy for the central government would be to send in military reinforcements.

A garrison of thousands of PLA troops has long been stationed in Hong Kong. The city's law states they can be deployed to "maintain public order" at the Hong Kong government's request.

The central government can also effectively suspend Hong Kong's laws if there is a "state of war" or "turmoil" that endangers national security.

"Given the resilient and undeterred nature of the protest movement and Beijing's inability to make concessions to civil society, the state's response will continue to be incremental -- and, I fear, increasingly violent," said J. Michael Cole, a Taipei-based senior fellow with the Global Taiwan Institute.

The last resort of sending in the PLA could spell financial disaster for Hong Kong and wholesale global condemnation for the Chinese Communist Party.

But, Cole said, "such considerations would have much less traction if the CCP concludes that the ongoing challenges in Hong Kong threaten its reputation and stability in China proper".