Opposition to the extradition bill has united an unusually wide cross section of Hong Kong against the proposal and sparked huge rallies.
The city's pro-Beijing leader Carrie Lam has so far refused to meet protester demands to withdraw or scrap the bill.
But on Friday Lam found herself facing calls from within her own political camp to reverse course and tamp down spiralling public anger.
Prominent pro-Beijing lawmaker Michael Tien openly called on Lam to postpone the bill.
"She would gain points instead of losing points," he told reporters. "Nothing is ever too late. New situations arise that would provide the basis for any leader to change their position. There's nothing wrong with that."
Tien's comments came as Lam's own advisor said pushing ahead with fast-tracking the bill through the city's legislature had now become "impossible".
"Personally I can see that it is impossible to discuss (the bill) when there is so much conflict on all sides. It is very difficult," Bernard Chan told RTHK radio.
"At the very least we should not escalate the antagonism," he added, although he stopped short of saying whether the bill should be scrapped.
Chan sits on the Executive Council -- the equivalent of a cabinet -- and was appointed by Lam two years ago to be a top advisor.
The comments are the first indication that supporters of the extradition law are now having second thoughts following a growing public backlash.
On Sunday, protest organisers said more than one million people came out for the largest protest the business hub has seen in decades.
Lam's refusal to press ahead with a debate on the bill in parliament on Wednesday sparked another huge protest that descended into violence and brought the city's commercial district to a standstill.
Young Hong Kongers, angered by years of sliding democratic freedoms in the city, have been at the forefront of the protests.
But the extradition plan has also received a barrage of criticism from legal bodies, business groups, religious figures and Western nations who fear the proposal would tangle both locals and foreigners up in China's politicised and opaque courts. —AFP
