Hong Kong leader Carrie Lam apologised on Tuesday for the political unrest that has shaken Hong Kong, but the pro-Beijing chief executive refused to cave in to demands for her resignation.

The semi-autonomous territory has been plunged into its biggest crisis in decades, with millions of people taking to the streets to demand the withdrawal of proposed legislation that would have allowed extraditions to mainland China.

Lam suspended the bill on Saturday after two massive rallies that saw isolated bouts of violence between the police and some protesters.

But that failed to quell public anger, and an even bigger rally on Sunday drew over two million people, organisers said.

“I personally have to shoulder much of the responsibility. This has led to controversies, disputes and anxieties in society,” Lam told a press conference.

“For this I offer my most sincere apology to all people of Hong Kong.”

Protesters have demanded that the bill be fully withdrawn, and for Lam to step down and apologise for police using tear gas and rubber bullets to disperse protesters last week.

They have also asked for all charges to be dropped against anyone detained during the protests.

But Lam gave no indication she was prepared to step down, saying instead she wanted to “continue to work very hard . .  . to meet the aspirations of the Hong Kong people”.

Without explicitly stating so, Lam indicated, however, that the extradition bill was unlikely to be revived given the public sentiment.

“I will not proceed again with this legislative exercise if these fears and anxieties could not be adequately addressed,” she said.

“If the bill . . . [does] not make the legislative council by July next year, it will expire . .   . and the government will accept that reality.”

Critics of the legislation fear it will entangle the people of Hong Kong in China’s notoriously opaque and politicised justice system, and threaten Beijing’s critics.

The mass protests also drew support from the city’s formidable business community, amid fears the law would damage Hong Kong’s reputation as a safe business hub.

While the extradition issue had been the spark for the mass rallies, the protest movement has since morphed into the latest expression of public rage in Hong Kong against both the city’s leaders and Beijing.