Lam's apology during a press conference came after tens of thousands of opponents sent her an ultimatum on Tuesday morning to meet their demands or face escalated protests, reports the South China Morning Post.
The statement, circulated on the encrypted messaging platform where 75,000 public members shared information about the anti-bill protests, listed four demands, including the complete withdrawal of the legislation that would allow those accused of certain crimes to be extradited to China.
"I understand how people feel... This incident lets me know I have to do better," she said.
"I have heard you loud and clear and have reflected deeply on what has transpired... I personally have to shoulder most of the responsibility... I offer my most sincere apology to all the people of Hong Kong."
Asked whether she regarded the violent clashes on June 12 as a "riot", to which she replied that her government never considered nor said that the participants, particularly young students, were rioters.
In the June 12 protests, hundreds of thousands of people poured into the streets to call for the bill to be cancelled, though at the time they only achieved a postponement of its second reading in the Legislative Council.
Police dispersed crowds in front of the legislature that day, firing tear gas and rubber bullets which left 81 people wounded, two of whom are in a serious condition, while 11 people were arrested, according to the authorities.
On June 15, Lam backed down and announced the suspension of the bill until further notice.
But the next day, a mass protest of about 2 million people was staged calling for her resignation and for the complete withdrawal of the legislation.
Tuesday was the third time in four days Lam has softened her stance since she announced the suspension of the extradition bill.
( With inputs from IANS )