Hong Kong is bracing for fresh rallies on Friday, which many fear could turn violent, as protesters gave city authorities until Thursday to meet their demands on the retraction of the city’s controversial extradition bill.

Anonymous messages have circulated on social media and messaging services calling for people to gather outside the government headquarters in the Admiralty business district to “escalate their actions” if the Hong Kong government fails to meet their demands by 5pm on Thursday. It called on people to strike, close shops and stay off school on Friday. On one popular chat platform alone, the message received nearly 93,000 “likes”. A user called this “Hong Kong’s last battle”.

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The messages started on Tuesday evening, after a press conference by the city’s leader, Carrie Lam, in which she offered a “sincere” apology but no more concessions. Security Secretary, John Lee, echoed his boss’ apology for the “anxiety and conflict caused” but also stopped short of making concessions.

Many in Hong Kong are angry that Lam has failed to address their requests. Protesters are demanding she fully withdraw the extradition law and investigate police brutality during the demonstrations, in which riot officers used rubber bullets and tear gas, injuring at least 72. They also want her to release those arrested, refrain from calling last week’s protest a riot, and resign.

On Saturday, after two large protests in one week, Lam suspended the controversial extradition bill, which many fear could see fugitives but also government critics extradited to mainland China for non-political charges. But many remain dissatisfied that she would not retract the bill on Tuesday. .

Facebook Twitter Pinterest Passer-by looks at notes and placards with messages of support for the protest against the extradition bill in Hong Kong. Photograph: Tyrone Siu/Reuters

Another anonymous statement calls more more radical actions. The message, titled “an apology statement to Hong Kong citizens from (a group of) fighters” posted Tuesday evening calls on people who wish to join the protests to be equipped with protective gear such as face masks, umbrellas and goggles and come with a “firm heart, cool head and to act accordingly as the situation emerges.” It also warned people who did not plan to join the protests to stay away from Admiralty on Thursday and Friday.

“Sorry, Hong Kong citizens,” it said. “Over the past two weeks, there have been two protests participated by more than one million people, there have also been many peaceful gatherings and one martyr has even protested with his death, but our five requests have still not been met. People will resist when they are pressured by the authorities, therefore we cannot rule out intensifying our fight.”

Many who responded to a Facebook post carrying the statement showed their concern. One said “I am heartbroken, please stay safe! Others warned that the authorities might have an excuse to crackdown on protests that turn violent. “Please don’t fall into their trap. Exercise restraint and stay peaceful!” said another posting.

Meanwhile, a group of university student union representatives urged people to surround the government headquarters on Friday morning to take part in peaceful, non-cooperation protests if the government fails to respond by Thursday afternoon. Asked by reporters whether they supported the individuals who threatened to take radical action, they said they respected them.

Young people interviewed by the Guardian over the past week said they felt they had run out of options as the government had ignored the huge protests that were over a million-strong.

Veteran politician Emily Lau warned that Hong Kong would quickly lose international support if there was violence . She believed the protesters would have more to lose. “Can you be more violent than the police or People’s Liberation Army? she said.

Veteran China watcher and journalist Ching Cheong worried that if the demonstrators resorted to violence, Chinese authorities would be justified to mobilise the army. Hong Kong s mini constitution, known as the Basic Law, allows military intervention by the Chinese army in a state of emergency, including “turmoil” which “endangers national unity or security and is beyond the control of the government” of Hong Kong, or when the city’s leader requests its help to maintain public order.

“I worry not only about bloodshed but that it would give the Chinese police or army reasons to intervene if the situation is declared a state of emergency,” he said.

He urged Lam to defuse the situation by formally retracting the bill and investigating police use of force on Wednesday, which has caused widespread resentment.

Amid the tense political atmosphere, the legislature has postponed debate on a proposed national anthem law until after its summer break, Radio Television Hong Kong reported.