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Protest organisers said almost 2 million people turned out on Sunday to demand that Lam step down in what is becoming the most significant challenge to China’s relationship with the territory since it was handed back by Britain 22 years ago.
It comes at a time when Chinese President Xi Jinping is grappling with a deepening U.S. trade war, an ebbing economy and regional strategic tension.
Hong Kong opposition politicians are echoing marchers' calls for both Lam and the law to go, even after she apologised for her government's handling of the bill, which would let suspects be sent to mainland China for trial for the first time.
"Her government cannot be an effective government, and will have much, much, much difficulties to carry on," veteran Democratic Party legislator James To told government-funded broadcaster RTHK.
"I believe the central people's government will accept her resignation."
However, the official China Daily said Beijing's leaders would continue to back Lam, as it lashed out at foreign "meddling" in the crisis.
China's support for Lam will "not waver, not in the face of street violence nor the ill-intentioned interventions of foreign governments," the newspaper said in an editorial.
While Lam delayed the bill, it has yet to be completely shelved, despite broad domestic and international concern that the status of Hong Kong as a financial hub could be eroded by changes to the rule of law.
"We cannot accept her apology, it doesn't remove all our threats," said social worker Brian Chau, one of several hundred protesters who stayed overnight in the Admiralty district around the government headquarters and legislature.
Some demonstrators cleared rubbish left after the vast, but peaceful, march while others sang 'Hallelujah', a gospel song that has become a feature of the protests against Lam.
The headquarters will stay closed on Monday, the government said. A smattering of uniformed police stood by without riot equipment, in a contrast to the recent violent skirmishes between police and protesters.
The movement against Lam is widely expected to get a boost on Monday morning, when one of the government's most strident critics, activist Joshua Wong, is set to be freed from jail.
Wong, 22, and his pro-democracy Demosisto group played a key role in the "Occupy" protests that galvanised the city in 2014.