Hong Kong’s leader Carrie Lam has said that a controversial bill allowing extradition to China is “dead” and that her government’s attempts to pass it, which sparked weeks of mass protests, were a “total failure”.

The city’s chief executive spoke at a news conference on Tuesday after yet another major demonstration saw tens of thousands turn out on Sunday, clashing with police outside the main train station for arrivals of visitors from mainland China.

Protest leaders and rights groups have issued five demands, including the formal withdrawal of the bill, immunity from prosecution for protesters and the immediate resignation of Ms Lam herself.

Ms Lam has previously attempted to placate them by saying the extradition bill “will die” when it is allowed to expire at the end of the current legislative term.

On Tuesday she accepted there were “lingering doubts about the government’s sincerity or worries about whether it would seek to bring the legislation back for a vote”.

But she said: “I reiterate here, there is no such plan. The bill is dead.”

Aftermath of protesters storming Hong Kong government HQ: In pictures Show all 15 1 /15 Aftermath of protesters storming Hong Kong government HQ: In pictures Aftermath of protesters storming Hong Kong government HQ: In pictures The lobby of the Legislative Council building in Hong Kong is seen covered in graffiti after it was stormed by protesters Getty Aftermath of protesters storming Hong Kong government HQ: In pictures Police officers stand guard at the Legislative Council building in Hong Kong after it was stormed by protesters EPA Aftermath of protesters storming Hong Kong government HQ: In pictures The colonial flag of Hong Kong hangs in the chamber of the Legislative Council after protesters stormed the building Reuters Aftermath of protesters storming Hong Kong government HQ: In pictures Police officers are seen behind cracked glass panels that were damaged by protesters trying to ram their way into the Legislative Council building EPA Aftermath of protesters storming Hong Kong government HQ: In pictures Shattered glass is seen on the outside wall of the Legislative Council of Hong Kong after protesters smashed their way in the building AP Aftermath of protesters storming Hong Kong government HQ: In pictures Riot police patrol the Legislative Council building in Hong Kong after it was stormed by protesters Getty Aftermath of protesters storming Hong Kong government HQ: In pictures Police officers inspect damage to the Legislative Council building in Hong Kong after it was stormed by protesters AFP/Getty Aftermath of protesters storming Hong Kong government HQ: In pictures A caricature of Hong Kong leader Carrie Lam is pasted on a pillar outside of the Legislative Council after protesters broke into the building Reuters Aftermath of protesters storming Hong Kong government HQ: In pictures Graffiti is seen in the chamber of the Legislative Council in Hong Kong after protesters stormed the building Getty Aftermath of protesters storming Hong Kong government HQ: In pictures Abandoned placards and litter is seen outside the Legislative Council building in Hong Kong after a protest on July 1 EPA Aftermath of protesters storming Hong Kong government HQ: In pictures A painting hung i the Legislative Council in Hong Kong is covered in graffiti after protesters stormed the building Getty Aftermath of protesters storming Hong Kong government HQ: In pictures A lift in the Legislative Council building is seen covered in graffiti and litter after protesters stormed the building Getty Aftermath of protesters storming Hong Kong government HQ: In pictures The chamber of the Legislative Council in Hong Kong after protesters stormed the building Getty Aftermath of protesters storming Hong Kong government HQ: In pictures A desk in the chamber of the Legislative Council in Hong Kong is covered in graffiti after protesters stormed the building AFP/Getty Aftermath of protesters storming Hong Kong government HQ: In pictures An area inside the Legislative Council building complex is strewn with litter and smashed glass after it was stormed by protesters Getty

As to the other demands, Ms Lam said it was up to the judicial system, not the executive, to deal with any offences committed by protesters and that an amnesty would go “against the rule of law in Hong Kong”.

And on her own position, she said: “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.

“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.”

Jimmy Sham and Bonnie Leung, two convenors of the Civil Human Rights Front, which has organised demonstrations, said protests would continue until the five demands were met, and that details would be announced at a later time.

Mr Sham accused Ms Lam of using “words to cheat the public”, adding that: “We cannot find the word ‘dead’ in any of the laws in Hong Kong or in any legal proceedings in the Legislative Council.”

Ms Leung said it was hypocritical of Ms Lam to suggest she was listening to the people when she has failed to meet with protest leaders. “The young protesters have been out in the street outside her house, outside government headquarters, for weeks, roaring to be heard,” she said.

Joshua Wong, a student activist who recently joined the protests after serving a prison term for his involvement in the 2014 Umbrella Movement, said he was “fed up with Carrie Lam’s wordplay”.

He repeated the demand for the bill to be “formally withdrawn”, saying that as long as it remained in the Legislative Council programme until July next year it was “a ridiculous lie” to call it dead.

And in a statement, Amnesty International said it was “long overdue for [Ms Lam] to give an unequivocal commitment that the extradition bill, which poses a real threat to human rights, will be withdrawn for good”.

The organisation called for an independent inquiry into the most violent protest on 12 June, which the Hong Kong government has referred to as a “riot”, saying that the “excessive use of force by police” on that day must be met with action.

The ongoing crisis reflects fears among many ordinary Hong Kong people that the city’s autonomy, guaranteed under the “one country, two systems” principle and enshrined in international law under the treaty that handed Hong Kong back to China from Britain, is being eroded.

The extradition bill in question would have allowed suspects in the city to be extradited to China, as well as many other countries and territories, on a case-by-case basis and with the approval of Hong Kong’s high court.

Ms Lam’s administration said the bill was necessary to prevent Hong Kong being used as a haven for criminals from the mainland and abroad, but critics feared it could be used to abduct political opponents of Beijing for show trials.

In the most recent protest on Sunday, people marched towards a high-speed railway terminal that links the city to the mainland, chanting “Free Hong Kong” and some carrying British colonial-era flags.