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* Students call for full withdrawal, Lam's resignation
* Lam rules out amnesty for protesters
* Says there is no plan to restart bill amendment process
* (Updates with reaction from lawmaker)
HONG KONG, July 9 (Reuters) - The extradition bill that sparked Hong Kong's biggest crisis in decades is dead, the territory's leader said on Tuesday, adding that the government's work on the legislation had been a "total failure," but critics accused her of playing with words.
The bill, which would allow people in Hong Kong to be sent to mainland China to face trial in courts controlled by the Communist Party, sparked huge and at times violent street protests and plunged the former British colony into turmoil.
In mid-June, Hong Kong leader Carrie Lam responded to protests that drew hundreds of thousands of people on to the streets by suspending the bill, but demonstrations that shut government offices and brought parts of the financial center to a standstill continued.
Her latest attempt to restore order did not satisfy many protesters who stood by demands that she completely withdraw the bill and accused her of playing word games.
"There are still lingering doubts about the government's sincerity or worries whether the government will restart the process in the Legislative Council," Lam told reporters on Tuesday.
"So, I reiterate here, there is no such plan, the bill is dead."
The bill triggered outrage across broad sections of Hong Kong society amid concerns it would threaten the much-cherished rule of law that underpins the city's international financial status.
Lawyers and rights groups say China's justice system is marked by torture, forced confessions and arbitrary detention, claims that Beijing denies.
University students who have been out in force during the protests rebuffed Lam's comments.
"What we want is to completely withdraw the bill. She is playing word games," said Chan Wai Lam William, general officer of the Student Union of Chinese University of Hong Kong.
Demonstrators have called for Lam to resign as Hong Kong chief executive, for an independent investigation into police actions against protesters, and for the government to abandon the description of a violent protest on June 12 as a riot.
"It is not a simple thing for CE (chief executive) to step down, and I myself still have the passion and undertaking to service Hong Kong people," Lam said when asked about the protesters' demands.
"I hope that Hong Kong society can give me and my team the opportunity and room to allow us to use our new governance style to response to people's demand in economy and in livelihood."
Hong Kong returned to Chinese rule in 1997 with the promise of a high degree of autonomy, but in recent years there has been growing concern about the erosion of those freedoms at the hands of Beijing.
Critics of the extradition bill fear Beijing could use it to crack down on dissent.
China has called the protests an "undisguised challenge" to the "one country, two systems" model under which Hong Kong is ruled that allows freedoms not enjoyed in mainland China, including the right to protest and an independent judiciary.
Fernando Cheung, a pro-democracy lawmaker who has been aligned with the protesters, said Lam's response was insufficient.
"She still doesn't get it. If she doesnt establish an independent inquiry commission, it's the death of her administration, not just the bill. The crisis cannot be settled without some heads rolling," he told Reuters.
Jimmy Sham, convenor of the Civil Human Rights Front, which has organized a series of protests, said Lam should meet the protesters' demands and stop using "words to cheat the public."
Chief executives of Hong Kong are selected by a small committee of pro-establishment figures stacked in Beijing's favor and formally appointed by China's central government. Lam's resignation would require Beijing's approval, experts say.
Lam said the June 12 protest, which saw police fire tear gas, rubber bullets and beanbag rounds at demonstrators, had not been given a label, but reiterated any decision to prosecute would be one for the justice department.
"Any demand that we should run an amnesty at this stage, that we will not follow up on investigations and prosecutions of offenders is not acceptable, because that bluntly goes against the rule of law in Hong Kong," she said.
. "..My sincere plea is: Please give us an opportunity, the time, the room, to take Hong Kong out of the current impasse and try to improve the current situation." (Additonal reporting by Farah Master and Vimvam Tong Writing by John Ruwitch Editing by Michael Perry and Nick Macfie)