Pro-democratic opposition newspaper Apple Daily called for fresh protests from Friday if Lam did not accept the demands by 5 p.m. on Thursday, a call which is being widely followed on social media.
One of Hong Kong's most prominent student activists, Joshua Wong, 22, who is widely known for his leading role in the 2014 pro-democracy "Umbrella" protests, told Efe news that they did not issue the ultimatum but were backing it.
"We have not set a deadline, but we will support and support what others do. This movement does not have a leader right now," said the young activist when asked about the call for protests.
"A lot of movement is expected in the next two weeks," he added in reference to fresh protests demanding Lam's resignation, the release of those who have been detained in demonstrations and the complete withdrawal of the legislation that would allow crime suspects sent to mainland China to stand trial.
"The government should begin listening to people and less to political leaders," he warned.
Meanwhile, Bonnie Leung, the spokesperson of Civil Human Rights Front, a coalition of about 50 organisations, told Efe news that "there are lots of actions initiated by different groups and individuals in the civil society" and added that her organization "would like to join them".
"But as we always stress, CHRF wants to do our best to make sure all participants will be safe legally and physically during any actions," she said.
The ultimatum, which calls for protesters to surround the government's headquarters on Friday in acts of civil disobedience if the demands are not met, has been supported by associations of university students and pro-democracy lawmakers.
On Tuesday, Lam at a press conference offered her "most sincere apology to all people of Hong Kong" and asked its citizens to give her another opportunity so that her government could rebuild trust.
The extradition bill has been met with opposition from various sectors of society on grounds that Hong Kong would lose its judicial independence and according to human rights organisations, it would allow activists, non-profit workers and journalists to be tried in a Chinese judicial system which offers no guarantees.
( With inputs from IANS )