HONG KONG - Hong Kong leader Carrie Lam apologised on Sunday (June 16) to the city's residents and promised to serve them better after tens of thousands took to the streets denouncing a Bill that would allow extradition to China.

The protesters, many of whom wore black, also called on Mrs Lam to step down.

They took over the main thoroughfare in front of the Hong Kong government headquarters in Admiralty on Sunday evening, demanding that the government scrap the planned amendments to the extradition law that many see as another sign of Beijing's creeping erosion of Hong Kong's rights and freedoms.

Organisers said nearly two million people showed up at the rally, while police said there were 340,000.

In response to Sunday's protest, the government issued a statement saying: "The chief executive admits that the inadequacies of the government has caused huge friction and dispute in the society, and has disappointed and saddened Hong Kong people. The Chief Executive apologises for this and promises to receive criticisms with utmost sincerity and humility and will improve to serve the public."

After intense public pressure, Mrs Lam announced last Saturday that the Bill would be indefinitely postponed. She also admitted that she had misread the public mood but stopped short of apologising.

Protesters on Sunday said they don't trust the government and want the Bill scrapped for good. They said they would continue their fight until they achieve their goal.

The protesters brought traffic to a standstill in parts of central Hong Kong, with thousands streaming in from Admiralty and Causeway Bay.

Many used their mobile phones as torches, shouting "stay strong Hong Kong" and "withdraw" in Cantonese. Hundreds more were shouting the same from pedestrian bridges above the road.

The 3km march to the government headquarters began in Victoria Park and went through Causeway Bay and Wan Chai as police closed off roads. The protest was peaceful, in contrast to last Sunday's huge protest which ended in violence.

Sunday's protest appeared to be well coordinated and organised. The crowd could be seen coordinating to clear a path for buses and an ambulance.

Hennessy Road in Causeway Bay, the popular shopping and tourism district, was closed to traffic in both directions, with protesters chanting "Step down, Carrie Lam" in Cantonese as they moved in the direction of Admiralty. Others lined the road holding red signs that read "stop killing us" in English and Chinese.

At one point, there was a mass rendition of "Do You Hear The People Sing", the pro-democracy anthem from the musical Les Miserables, Bloomberg reported.

Local student Herman Mo, 29, told The Straits Times that Mrs Lam needs to step down and take responsibility for the violent protests.

"The government has not taken the people's opinion into consideration when it should. I believe if Carrie Lam refuses to step down, we will continue to protest," he said.

Along the protest route, supply stands were set up, with volunteers giving out bottles of water, snacks and even umbrellas. Entire families with children were also seen heading towards Causeway Bay.

Ms Hebe Lau, in her 30s and working in finance, told ST that she was at the rally to send a signal to the Hong Kong government that the Bill must be withdrawn.

"Postponing is just an excuse to all Hong Kong citizens and cannot even be considered a victory at all," she said. She was among thousands who gathered at Victoria Park in sweltering summer heat to join the march.

In the self-ruled island of Taiwan, which China claims as its own, about 5,000 people rallied outside the parliament building in Taipei on Sunday with banners saying, "No China extradition law" and "Taiwan supports Hong Kong", Reuters reported.

Some of the protesters in Hong Kong also waved Taiwan flags.

Besides calling for the now-postponed extradition Bill to be withdrawn completely, the protest in Hong Kong on Sunday also called on the city's embattled leader to resign, a week after a million people came out to oppose the legislation.

Following a week that had protesters surround the legislature to prevent lawmakers from discussing the Bill - resulting in clashes that saw police deploy tear gas and rubber bullets - Mrs Lam last Saturday that the Bill would be indefinitely postponed, but not scrapped.

In an hour-long press conference, Mrs Lam also defended the police, who earlier said they had no choice but to use force against violent protesters who surrounded the Legislative Council Complex last Wednesday.

But protest leaders say the move to suspend the Bill indefinitely is simply an attempt to kick the issue into the long grass.

"We have been lied to many times before when the government said they will postpone projects. But after the social pressure has eased, they go on to do it anyway," said Civil Human Rights Front (CHRF) vice-convenor Bonnie Leung on Saturday.

A coalition of pro-democracy lawmakers and advocacy groups, CHRF has been at the forefront of the movement opposing the Bill. They have vowed to continue protesting until the Bill is completely withdrawn.

The group is also calling on Mrs Lam to step down, saying that her reaction to the public furore is "arrogant, ignorant and indifferent".

Anger has also been fanned by Mrs Lam and senior officers calling the street demonstrators "rioters". The group is calling for police to drop charges against anyone arrested for rioting and other offences linked to last Wednesday's clashes.

The extradition Bill was initially scheduled to be debated in the Legislative Council (LegCo) last Wednesday but was postponed twice after thousands of protesters heeded calls to surround the government headquarters in Admiralty.

Police said they had no choice but to use force to meet violent protesters who besieged their lines outside the city's Parliament, but critics say it was excessive against peaceful, unarmed and mostly young protesters.

"We will adopt the most sincere and humble attitude to accept criticisms and make improvements, so that we can continue to connect with the people of Hong Kong," Mrs Lam told reporters at a press conference on Saturday to announce the Bill's delay.

But she insisted that the Bill is not being withdrawn, stressing that the government remains focused on the Taiwan murder case and loopholes in the city's extradition agreements.

"We might not be able to deal with the first one. But we still need to plug loopholes. So at this stage, I don't think the Bill can be withdrawn," she said.

If passed into law, the Bill would allow for case-by-case handovers of fugitives to jurisdictions with whom Hong Kong does not have an extradition agreement.

The Bill was first mooted in February following the murder of a Hong Kong woman by her Hong Konger boyfriend in Taiwan. The man, Chan Tong Kai, escaped prosecution in Taiwan by simply returning home, since Hong Kong does not have an extradition agreement with Taiwan.

If passed, the Bill will also create a legal mechanism allowing for suspected criminals to be handed over to the mainland, which many fear could be used on political dissidents and activists.

The Hong Kong government said safeguards have been added since the Bill was tweaked after consultation, following pushback from critics. One of the six additional safeguards is raising the threshold for offences to be covered by extradition to imprisonment for seven years or more, from the initial three years.

Among other things, if the surrender involves a Hong Kong permanent resident and the resident makes an application, the government will assist the sentenced person in serving his sentence in Hong Kong.

Mrs Lam has said that the extradition arrangement is in line with international norms.

Under "one country, two systems", Hong Kong has a separate Constitution and judiciary from the mainland, with its residents guaranteed liberties unseen in China, including a free press and the right to protest.

But there are growing concerns that this has been gradually eroded in the last few years: booksellers who specialise in salacious tomes about the Communist Party leadership have disappeared and resurfaced in the mainland confessing to crimes; a proposed law barring insult of the Chinese national anthem is making its way through the LegCo; and a pro-democracy political party was recently outlawed.