Lam told a news conference that China's central government "understands, respects and supports" her government in the entire process.
Withdrawal of the bill meets one of protesters' five key demands, but activists have vowed not to yield until the government fulfills all of them. Those also include an independent investigation into allegations of police brutality during the protests, the unconditional release of those detained, not labelling the protests as riots, and direct elections of the city's leader.
The massive but peaceful demonstrations began in June against the legislation, which would have allowed criminal suspects to be sent to mainland China for trial, but clashes with police have become increasingly violent as the demands evolved into a wider call for democracy.
Demonstrators threw gasoline bombs at officers last weekend protests and police retaliated with water cannons, tear gas, rubber bullets and batons. Nearly 1,200 people have been detained so far.
Lam reiterated that the government cannot accede to the protesters' other demands. She said the police watchdog agency will be impartial and best suited to investigate alleged police misconduct, and that releasing detainees without charges would be "unacceptable."
She denied making a U-turn on the bill, noting that she suspended the bill in mid-June, days after the protests began, and in July declared the bill effectively dead.
"It is not exactly correct to describe this as a change of mind," she said when asked why it took her so long to kill the bill. "As far as the substance is concerned, there is simply no plan to take forward the bill."
She said the bill will be formally withdrawn without any need for debate and voting in the legislative council, which resumes its meeting next month and is packed with pro-Beijing lawmakers.
"The decision is one of Hong Kong's...government," she said. "Throughout the whole process, the central people's government took the position that they understood why we have to do it. They respect my view, and they support me all the way."
Lam voiced hope that the bill's withdrawal and other measures to address society discontent will provide an "important basis" to open dialogue to seek a way out of the impasse.
Lam, who was elected as the city's chief executive by a pro-Beijing committee of Hong Kong elites, has come under withering criticism for pushing the extradition bill. Many in Hong Kong saw the bill as a glaring example of the city's eroding autonomy since the former British colony returned to Chinese control in 1997.
The bill's withdrawal, widely seen as a bid to halt the unrest that could embarrass China during its National Day celebrations on Oct. 1, has been slammed as "too little, too late" by both government supporters and demonstrators.
Dozens of demonstrators took to the streets in some areas overnight shouting "five key demands, not one less." Local media reported that protesters built barriers near a police station at Mong Kok and pointed laser beams at police but fled after riot police confronted them.
Students also reportedly staged protests outside some schools Thursday, forming human chains across streets to show their support for those detained by the government.
More protests are planned for the weekend, including another one at the airport. The airport has been the site of several protests, causing flight disruptions and cancelations, as protesters seek to drum up international support.
The mostly young protesters say a degree of violence is necessary to get the government's attention after peaceful rallies were futile. Chinese officials have warned that Beijing will "not sit idly by" if the situation worsens.
The European Union said it hopes the decision to withdraw the extradition bill will help end the violence.
EU foreign policy chief Federica Mogherini's office said in a statement that Lam's action "opens up space to work towards a peaceful and enduring solution to the unrest in Hong Kong."
It said "respect for fundamental rights and freedoms, and the independence of the judiciary, remain essential for the development of Hong Kong, and should be upheld in line with the Basic Law and China's international commitments."
The statement said the EU plans to closely monitor "the impact on EU citizens and on EU economic interests in Hong Kong."
The prolonged protests, which sparked fears of a military intervention by China, have hurt businesses in Hong Kong and led to a plunge in tourism.
The Hong Kong government sought to assuage international jitters, vowing to "achieve a peaceful, rational and reasonable resolution" to the crisis in a full-page advertisement Thursday in the Australian Financial Review.
It said it is committed to the "one country, two systems" policy to ensure Hong Kong remains free and open. It called the unrest part of a "complex social, economic and political jigsaw puzzle."
"It is a puzzle that we will solve on our own. And it may take time," the advertisement said. "We will no doubt bounce back. We always do."