HONG KONG — On Sunday, protesters filled Hong Kong’s streets for a second time in a massive demonstration calling on their government to withdraw a proposal to allow extraditions to China, and for Hong Kong chief executive Carrie Lam to step down.

Days later, on Tuesday, Lam offered a “very sincere apology” to the people of her territory for the “anxiety” caused by plans for the legislation. She also said it was “very unlikely” that the extradition plans, which she suspended last week, could be introduced again before the end of the Hong Kong legislature’s term in July 2020.

Lam, however, will not fully withdraw the legislation and said she wants to continue to serve the public.

“I have heard you loud and clear and have reflected deeply on all that has transpired,” she said, her voice shaking at times as she delivered a statement before a packed room of reporters.

The address marked the latest embarrassment for Lam, who has become increasingly isolated in the city and criticized even by pro-Beijing lawmakers in her camp. It also underscored the difficulty of the chief executive’s position and the tightrope she must walk to keep her own citizens happy as well as the authorities in Beijing.

The events of the past week, analysts say, have made Lam less effective in pushing through policies Beijing wants. Chinese authorities have significant say over who becomes Hong Kong’s top leader.

Lam “would be a lame duck, as she may not dare to implement controversial policies anymore to avoid provoking the opposition,” said Ivan Choy, a political scientist at the Chinese University of Hong Kong. Yet, he said, “Beijing may not be ready to find a replacement for her immediately.”

Lam said Tuesday that she has to “shoulder much of the responsibility” for the problems that the plans have caused.

“I should have done better,” she said.

The Civil Human Rights Front, the group that helped facilitate the massive rallies, told reporters after Lam’s statement that her words were nothing new. The group said it will discuss any future action and the way forward with a broader camp of pro-democracy legislators and activists.

Proposals pushed forward by Lam’s government have sparked a massive upheaval in Hong Kong. On Sunday, organizers said almost 2 million people marched through the streets of the city until late at night — for the second time in a week. They were protesting an earlier police crackdown on demonstrators and demanding that Lam step down and withdraw the extradition bill rather than suspend it.

Opposition to the bill has reinvigorated a pro-democracy movement that is deeply suspicious of Beijing’s creeping control of the semiautonomous territory and determined to resist it. The extradition bill, many think, would end a crucial “firewall” between Hong Kong’s independent judiciary and mainland China.

Critics fear it would mark the end of the “one country, two systems” framework the territory has operated under since it was returned from the British to China in 1997 under a promise of significant autonomy, including its own immigration and legal system.

When Lam announced Saturday that she would suspend the extradition bill, she gave a full-throated defense of its goals, which she said were “laudable” and needed to “close a loophole” in Hong Kong law. On Tuesday, however, her tone was significantly more conciliatory — offering no justification for the bill, but still declining to fully withdraw it.

Her government, she said, will try to address “fears and anxieties” about the measure before she decides how and when to move forward with the proposals.

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

Timothy McLaughlin in Hong Kong contributed to this report.

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