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The extradition bill, which would cover Hong Kong's 7 million residents as well as foreign and Chinese nationals in the city, was seen by many as a threat to the rule of law in the former British colony.
Around a million people marched through Hong Kong last Sunday to oppose the bill, according to protest organisers. Protests continued through the week and were met with tear gas, bean bag rounds and rubber bullets from police, plunging the city into turmoil and piling heavy pressure on Lam.
"After repeated internal deliberations over the last two days, I now announce that the government has decided to suspend the legislative amendment exercise, restart our communication with all sectors of society, do more explanation work and listen to different views of society," Lam told a news conference.
She said there was no deadline, effectively suspending the process indefinitely.
Cracks began to appear on Friday in the support base for the extradition bill with several pro-Beijing politicians and a senior advisor to Lam saying discussion of the bill should be postponed for the time being.
Lam had not appeared in public or commented since Wednesday. She met pro-Beijing lawmakers to explain her pending announcement earlier on Saturday.
Backing down from efforts to drive the bill through the city's legislature by July would have been unthinkable last week when the law's passage seemed inevitable as Lam remained defiant.
Beyond the public outcry, the extradition bill had spooked some of Hong Kong's tycoons into starting to move their personal wealth offshore, according to financial advisers, bankers and lawyers familiar with the details.
And senior police officers have said Lam's refusal to heed public opinion was sowing resentment in the force, which was already battered by accusations of police brutality during the 2014 pro-democracy "Umbrella" civil disobedience movement.
Michael Tien, a member of Hong Kong's legislature and a deputy to China's national parliament, said a total withdrawal of the bill would not be possible.
"The amendment is supported by the central government, so I think a withdrawal would send a political message that the central government is wrong. This would not happen under 'one country, two systems'," he told Reuters, referring to the model under which Hong Kong enjoys semi-autonomy.
Organisers of last Sunday's protest march are planning another march this Sunday.
In addition to calling for the bill to be completely dropped, they would also be pushing for accountability of the police for the way protests have been handled.
Lam has said the extradition law is necessary to prevent criminals using Hong Kong as a place to hide and that human rights will be protected by the city's court which will decide on the extraditions on a case-by-case basis.
Critics, including leading lawyers and rights groups, note that China's justice system is controlled by the Communist Party, and marked by torture and forced confessions, arbitrary detention and poor access to lawyers.
Last Sunday's march was the biggest political demonstration in Hong Kong since people poured into the streets 30 years ago to protest against the bloody suppression of pro-democracy demonstrations centred around Tiananmen Square on June 4, 1989.
Hong Kong is governed by China under a "one country, two systems" deal that guarantees it special autonomy, including freedom of assembly, free press and independent judiciary.
Many accuse Beijing of extensive meddling since then, including obstruction of democratic reforms, interference with elections and of being behind the disappearance of five Hong Kong-based booksellers, starting in 2015, who specialised in works critical of Chinese leaders.
The Chinese government has denied that it has overreached in Hong Kong.