"I think it is impossible to discuss (the bill) under such confrontation. It would be very difficult," the South China Morning Post quoted Executive Council convenor Bernard Chan as saying.
"At the very least we should not escalate the antagonism."
Chan advised Chief Executive Carrie Lam's government to re-evaluate the situation in light of violent clashes between police and protesters after a mass rally against the bill brought hundreds of thousands onto the streets.
Chan also admitted he had underestimated the backlash from the business community over the proposed legislation, which would allow the transfer of fugitives to jurisdictions that Hong Kong does not have an extradition agreement with, including mainland China.
The adviser's statement comes after tens of thousands of protesters, mostly in their 20s, on Wednesday brought part of the city to a standstill by occupying key roads to besiege the legislature and prevent it from debating bill, reports the South China Morning Post.
The protest ended in clashes with police, which left more than 80 people injured as officers fired tear gas, rubber bullets and beanbag rounds to disperse the crowd.
Eleven people were arrested.
Before the protests escalated on Wednesday, Lam had insisted the government would push ahead with the bill.
( With inputs from IANS )