Lam called for the public to give her government “another chance” in explaining the need for the bill.
She said she didn’t want to see any more injuries from clashes.
The chief executive stressed the bill had stemmed from her passion for Hong Kong and said she regretted deficiencies in her and her government’s work had stirred up controversies after the relatively calm period of the last few years.
“As a free open pluralistic society Hong Kong needs such a spirit of mutual respect and harmony in diversity,” she said.
Lam would listen to public views on the legislation, which would potentially allow someone in Hong Kong to be extradited to mainland China for the first time.
The announcement was timed to defuse anger in the city ahead of a second planned protest march through the city on Sunday that had been approved by police.
There had been growing calls through the week for Lam to resign.
Anthony Dapiran, the author of City of Protest, wrote on Twitter that it was unclear what would happen with the bill and if Lam was “being deliberately vague with the objective of avoiding another big protest tomorrow”.
The urgency of passing the bill within this term of parliament had disappeared after pro-Beijing members of the Legislative Council had also supported the delay, Lam said.
She was “saddened and felt regret – we will sincerely and humbly accept criticisms and improve”, she told assembled reporters.
She refused to apologise for the way police handled Wednesday’s protest and said police were carrying out their duties.
“It was reasonable and natural for police officers to enforce the law and it is also their mission to do so,” she said.
Earlier on Saturday the organisers of the march to be held on Sunday – a week since an estimated 1 million Hong Kong people took to the streets to oppose the extradition bill – said they would fight on until the bill was removed.
Civil Human Rights Front Jimmy Sham said people wanted the bill withdrawn and Lam to also withdraw her description of Wednesday’s illegal protest as a “riot”.
The riot description will see protesters arrested by police face potential jail sentences.
Unions have also supported the march which may be a test of the level of anger at how police handled Wednesday’s protest.
The Hong Kong police were criticised by local and international human rights groups for releasing 150 rounds of tear gas on protesters and using rubber bullets and beanbag rounds.
“Hong Kong people will not forget, Hong Kongers will fight on until the bill is withdrawn,” said Sham.
Mainland Chinese vice premier Han Zheng met with Lam in Shenzhen, the mainland city adjacent to Hong Kong, on Friday night, Sing Tao newspaper reported.
Beijing had already moved to distance itself from the extradition bill in the week of the violent protests on Wednesday, with the Chinese ambassador to Britain Liu Xiaoming telling the BBC it was not Beijing’s bill and had been initiated by Lam.
Yet Beiing media had staunchly supported the bill and attacked its opponents as debate became more heated in Hong Kong this year.
In the press conference on Saturday, Lam’s first media appearance since the protests on Wednesday, she repeated that she doesn’t want Hong Kong to become a safe haven for criminals.
Kirsty Needham is China Correspondent for The Sydney Morning Herald and The Age.