The protesters, the vast majority of whom were dressed in black as a symbol of what they consider to be a loss of democracy in Hong Kong, also urged that Lam, who has only suspended the bill temporarily, must condemn the excessive use of police force during the June 12 protests, reports Efe news.
Sunday's protest, which left Victoria Park and was heading towards the Legislative Council headquarters, also held a minute's silence for the death of a young man who fell from a scaffolding on Saturday night while trying to put up a poster, and many were seen to wear bows and flowers as a sign of mourning.
Youths along with families and children participated in the protest carrying banners with the slogans "Stop the violence, we are not rioters" and "No to police brutality" amid demands for all charges to be dropped against those arrested during protests.
Lam on Saturday backed down and announced the suspension until further notice of the controversial legislative proposal that would allow those accused of certain crimes to be extradited to China.
Lam's change of stance, which had strongly been in defence of the bill, came after meeting her government and after some political leaders urged her to postpone it or suspend it.
Sunday's march is a follow-up to the June 12 protests, when 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.
Hours before the march began on Sunday, the Civil Human Rights Front expressed its support for the general strike called in Hong Kong by trade unions on June 17 and urged Hong Kong citizens to join it.
Proposed in February, the bill passing into law would allow the chief executive's headquarters and the Hong Kong courts to process extradition requests from jurisdictions without prior agreement - in particular mainland China and Taiwan - and without legislative supervision.
Opponents of the bill, which include a broad spectrum of Hong Kong society, fear that the new law could mean that local activists, critical journalists and dissident residents of Hong Kong could also be sent to mainland China for trial.
( With inputs from IANS )