Hong Kong(CNN) Hong Kong's embattled leader Carrie Lam has finally fully withdrawn a controversial bill that allowed extradition to mainland China and sparked three months of dramatic protests in the financial hub.

The decision to cave in to one of protesters' five core demands marked a dramatic U-turn for Lam, who for months has refused to withdraw the bill.

"We must find ways to address the discontent in society and look for solutions," Lam said in a a video statement Wednesday evening. "After more than two months of social unrest, it is obvious to many that this discontentment extends far beyond the bill."

But Lam refused to give ground on protesters' four other demands, including greater democracy for the city and an independent commission into police conduct, saying all investigations would be carried out by the existing Independent Police Complaints Council (IPCC).

Instead, she announced the addition of a former education bureau chief and former judge to the IPCC. Lam said the government's priority now was to restore law and order to Hong Kong. "Let's replace conflicts with conversations and let's look for solutions," she said.

Lam suspended the extradition bill in June after more than 1 million people marched against it, with protesters surrounding the city's legislature on the day of its planned second reading.

That suspension did not satisfy protesters, who demanded the bill's complete withdrawal -- making it harder for the government to rush the law through at a later date. A withdrawn bill would need to go back to the beginning of the legislative process, whereas a suspended one could resume where it left off.

In recent weeks, protesters' tactics have become increasingly violent as young people felt the government was refusing to consider their demands.

Pro-Beijing lawmaker Michael Tien said that Lam's withdrawal may not stem their anger. "I believe the withdrawal of the bill ... may be too late because this movement has become more than the bill," he said.

Activist Joshua Wong, who was last week arrested in a police sweep of activists and opposition politicians, wrote on Twitter: "Carrie Lam's repeated failure in understanding the situation has made this announcement completely out of touch - She needs to address to ALL Five Demands: STOP PROSECUTION, STOP CALLING US RIOTERS, INDEPENDENT INQUIRY OF POLICE and FREE ELECTION!"

Lam not resigning

Earlier this week, Lam denied that she had offered to resign over her handling of the crisis after a recording published Monday night of her at a meeting with business leaders was leaked to Reuters. On the tape, she can be heard saying she would have quit "if I have a choice."

Speaking to reporters Tuesday, Lam said she had not "contemplated to discuss a resignation" with her mainland superiors.

In the recording, Lam can be heard saying the bill was "not something instructed, coerced by the central government."

"If I have a choice, the first thing is to quit, having made a deep apology," she said. "We were not sensitive enough to feel and grasp (the) huge degree of fear and anxiety amongst people of Hong Kong vis-à-vis the mainland of China."

"For a chief executive to have caused this huge havoc to Hong Kong is unforgivable," Lam added.

That may remain the view for many Hong Kongers even after the formal withdrawal of the bill. Many will be asking why it took three months of unprecedented unrest, violence and damage to the city's economy for the government to upgrade the bill from "suspended" to "withdrawn," despite repeatedly insisting that it had no future and would not be reintroduced.

Lam may be hoping that the move will put a lid on the protests ahead of October 1, when China will celebrate National Day and mark 70 years of the People's Republic.

But whether this will be the case remains highly uncertain.

"The nature of the protest movement has transformed over the last 13 weeks," said Adam Ni, a China researcher at Macquarie University in Sydney.

"She will have to take further steps, such as setting up an independent inquiry into police conduct. If she does not take further steps, then we can expect the protests to continue."