Protesters have called for the unpopular Lam to stand down as leader, but Li Keqiang said Beijing would give "unwavering support" to her government. (AFP)

China’s premier told beleaguered Hong Kong leader Carrie Lam on Monday that she had Beijing’s “unwavering support” after a huge rally earlier this month and her government’s thrashing at recent local elections.

The city has been upended by six months of massive pro-democracy protests that have seen violent battles between police and hardcore demonstrators, as well as regular transport disruption.

Protesters have called for the unpopular Lam to stand down as leader, but Li Keqiang said Beijing would give “unwavering support” to her government to maintain the “long-term prosperity and stability in Hong Kong”.

“The central government fully recognizes the efforts you and the SAR (special administrative region) government have paid,” said Li, at a meeting with Lam in the Hong Kong Hall of the imposing Great Hall of People in Beijing.

He said Lam’s government had “tried its best to maintain social stability” amid “an unprecedentedly severe and complicated situation.”

But he also called for the Hong Kong government to “step up studies of the deep-seated conflicts and problems that hinder Hong Kong’s economic and social development” in order to restore calm to the city.

“Hong Kong is yet to get out of its plight. The SAR government must continue its hard work, stop violence and subdue chaos according to laws and restore order,” Li told Lam.

The city’s leader is in Beijing for an annual visit, and is set to meet President Xi Jinping later Monday.

At the meeting with Li, she said she was grateful for the premier’s “care for Hong Kong”.

The semi-autonomous city is ruled under the “one country, two systems” principle, which gives the territory rights unseen on mainland China — rights protestors say are steadily being eroded.

The past month had seen a lull in the violence and vandalism in the city, after pro-democracy parties won a landslide in local council elections.

A week ago, around 800,000 people marched peacefully through the city’s streets, urging the government to respond to their five demands — which include an independent inquiry into the police, an amnesty for those arrested, and fully free elections.

But public anger remains as Beijing and Lam show no sign of giving further concessions despite the election success.

This weekend the relative calm was broken by clashes between black-clad pro-democracy protesters and Hong Kong police in some of the city’s shopping malls.

And earlier this week an international panel of experts hired to advise Hong Kong on the police response to protests announced they were quitting, saying the watchdog was not fit for purpose “in a society that values freedoms and rights”.