The bill allowing Hong Kong residents to be sent to mainland China for trials sparked massive protests that have rocked the city since June. Lam had suspended the bill, but protesters wanted it entirely withdrawn.
Lam also reportedly announced an independent study to probe the city's social issues.
"For more than two months, protests arising from the Fugitive Offenders Bill have continued," Lam said in a prerecorded message translated by the South China Morning Post. "Our citizens, police and reporters have been injured during violent incidents."
"There have been chaotic scenes at the airport and MTR stations; roads and tunnels have been suddenly blocked, causing delay and inconvenience to daily life," Lam continued. "Visitors wonder whether our city is still a safe place for travel or business. Families and friends have been under stress, and arguments have flared."
She added: "For many people, Hong Kong has become an unfamiliar place. Incidents over these past two months have shocked and saddened Hong Kong people. We are all very anxious about Hong Kong, our home. We all hope to find a way out of the current impasse and unsettling times."
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The Hong Kong stock market soared 4 percent, boosted by news of the bill withdrawal.
Lam — who has come under fire for pushing the extradition bill, which many in Hong Kong see as an example of the city's eroding autonomy since the former British colony returned to Chinese control in 1997 — said Tuesday that Hong Kong's "one country, two systems" formula would be upheld.
"I have never tendered a resignation to the central people's government. I have not even contemplated to discuss a resignation...the choice of not resigning was my own choice," Lam said when asked why Beijing refused to let her quit. "I know it is not going to be an easy path, and that's why I have said that I have not given myself the choice to take an easier path and that is to leave."
Lam was elected as Hong Kong's chief executive by a pro-Beijing committee of Hong Kong elites, and the mainland government has spoken in support of her government and the city's police force throughout the protests.
The Associated Press contributed to this report.