Hong Kong’s embattled leader, Carrie Lam, has vowed to use “stern law enforcement” to stamp out violent protests, a day after she made a dramatic announcement to formally withdraw an extradition bill that has ignited months of protests.

At a press briefing on Thursday, Lam said the purpose of her decision to formally withdraw the suspended bill was to “zhibao zhiluan” (“put a stop to violence and chaos”) – a phrase often used by mainland Chinese officials when condemning the protests in Hong Kong.

“To step out of the impasse, the most important thing right now is to stop the violence and to sternly enforce the law,” she said. “If there is still violence going on every day, it will affect the city’s operation and people’s everyday lives.”

Lam announced on Wednesday evening in a televised message that her government would formally withdraw a controversial extradition bill that has plunged the territory into its biggest political crisis in decades.

But many ordinary Hong Kong residents and protesters, infuriated by the police’s excessive use of force in the past three months, said what mattered more to them was for the government to investigate police wrongdoing.

Quick Guide What are the five demands of the Hong Kong protesters? Show The complete withdrawal of the proposed extradition bill Hong Kong’s leader, Carrie Lam, has said her government will formally withdraw the bill that ignited months of protests. Hong Kong residents had feared it could be used by China to extradite people for political reasons. They want guarantees that it cannot be reintroduced at a later date. Withdrawal of the use of the word 'riot' in relation to the protests Protesters want the government to officially recognise that their movement has been a series of legitimate protests, rather than a riot, as has been stated in official communications. Unconditional release of arrested protesters and charges against them dropped Hundreds of people have been arrested in recent weeks, and the protesters are demanding that all of them be freed, and that no convictions should stand against any of them. An independent inquiry into police behaviour Police use of force has escalated since the demonstrations began, while protesters have also resorted to increasingly violent measures. Demonstrators say an inquiry into police brutality is the number-one priority. Implementation of genuine universal suffrage Hong Kong's chief executive is currently selected by a 1,200-member committee, and nearly half of the 70 legislative council seats are filled by limited electorates representing different sectors of the economy. The protesters want to be able to vote for their leaders in free and open democratic elections. Photograph: Anushree Fadnavis/X06783

During past months, police increasingly used water cannons, teargas, rubber bullets, beanbag rounds and severe beatings to quell protests, and also chased protesters into residential areas, metro stations and even ferry piers. Protesters have also thrown molotov cocktails at police, and vandalised and set public facilities on fire.

Many interviewed by the Guardian have said the escalating police brutality and the government’s hostility towards ordinary people in past months have hurt them deeply and made it hard for them to trust the authorities again. Police have arrested nearly 1,200 people so far.

On Thursday, Lam again rejected protesters’ demands to set up an independent body to investigate police use of force, and said it was impossible to give in to demands for an amnesty for those arrested, saying: “The government cannot do things that are against the rule of law.”

The protests, which started in early June, have morphed into a broader, and increasingly violent, anti-government movement, with animosity between police and protesters reaching boiling point.

Lam’s comments indicate that the government will continue to use hardline measures to deal with protesters, but many protesters vowed to continue demonstrating so long as the government refuses to investigate police’s abuse of power.

Chief executive Carrie Lam Photograph: Jérôme Favre/EPA

Just hours after Wednesday’s bill withdrawal, dozens shouted slogans and set up makeshift barricades outside a police station in the Mong Kok district demanding Lam meet all of their political demands. On Thursday morning, students from several secondary schools formed human chains outside their schools to protest against recent police brutality.

Lam also refused to step down, reiterating that she had “a sense of responsibility to help Hong Kong to ‘zhibao zhiluan’ (“put a stop to violence and chaos”)” and to get back to normal.

Lam however sidestepped a reporter’s question about whether the government would launch an emergency law with sweeping powers if protests did not stop. After Lam’s announcement, a pro-Beijing politician suggested that if protests continued, the authorities should invoke the Emergency Regulations Ordinance, which enables the government to impose draconian measures, including censorship and suppression of publications and communications, to quell unrest.

The withdrawal, which marks a u-turn after months of vows not to back down to the protesters, comes less than a month before China celebrates its national, day on 1 October, the 70th anniversary of the founding of the People’s Republic of China.