HONG KONG - Hong Kong chief executive Carrie Lam on Tuesday offered a "very sincere apology" to the people of her territory for the "anxiety" caused by plans for legislation to allow extraditions to mainland China, days after a second massive demonstration called for her to withdraw the bill and step down.

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 as demonstrators have demanded, 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.

Her address marked the latest embarrassment for Lam, who has found herself 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.

She added 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 facilitated 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 a police crackdown on protesters earlier last week and demanding that Lam step down and fully 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 over their semiautonomous territory and determined to resist it. The extradition bill, many believe, would end a crucial "firewall" between Hong Kong's independent judiciary and mainland China and mark the end of the "one country, two systems" framework that Beijing pledged when the former British colony was handed over to China in 1997.

When Lam announced she would be suspending the extradition bill on Saturday, 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 bill 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.

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The Washington Post's Timothy McLaughlin in Hong Kong contributed to this report.