A number of Hong Kong Chief Executive Carrie Lam's advisers have urged her to delay plans for a controversial change in extradition laws.
However, others still back the process and there is no evidence Ms Lam intends to delay.
Key adviser, Bernard Chan, favoured a pause as the "intense divisions" made it impossible to push on.
Protests were held this week to oppose a bill that could see some criminal suspects extradited to mainland China.
Hundreds of thousands took to the streets on Sunday and Wednesday. Dozens of people were injured when Wednesday's demonstration turned violent.
Hong Kong is a former British colony, but was returned to Chinese rule in 1997 under a "one country, two systems" deal that guarantees it a level of autonomy.
What are the divisions?
Mr Chan, who is a member of the Executive Council, the key advisory body to Ms Lam, told Cable TV he did not think formal discussion of the bill - the step before a final vote - should continue at the moment.
"At a time when there are such intense divisions - to keep discussing this issue, the difficulty is very high," he said.
Non-official Exco member Lam Ching-choi has also supported a step back, as has pro-Beijing lawmaker, Michael Tien, who said: "She would gain points instead of losing points."
Others want to proceed, including influential Exco member Regina Ip, the South China Morning Post has reported.
Ms Lam has herself stood by the bill.
What are the controversial changes?
The changes would allow for criminal extradition requests from authorities in mainland China, Taiwan and Macau - decided on a case-by-case basis by Hong Kong courts.
It comes after a high-profile case where a Hong Kong man was accused of murdering his girlfriend on holiday in Taiwan but could not be extradited.
Hong Kong officials, including Ms Lam, say the bill is necessary to stop the city being a safe haven for criminals.
But many fear the law could be used to target political opponents of the Chinese state in Hong Kong.
Opposition activists also cite the alleged use of torture, arbitrary detentions and forced confessions in mainland China.
How did protests unfold?
A large-scale march, which organisers said drew more than one million people, was held on Sunday.
Then on Wednesday tens of thousands gathered to blockade streets around government headquarters to try to stop the second reading, or debate, of the extradition bill.
Tensions boiled over and 22 police and 60 protesters were injured. Authorities say 11 people were arrested.
The police, who used tear gas and rubber bullets, have been accused of excessive force by some rights groups.
Ms Lam has not spoken publicly since Wednesday when in a tearful address, she labelled the protests "organised riots"
Activists are planning further demonstrations this weekend.
Why are people angry about the plan?
Hong Kong was a British colony from 1841 until sovereignty was returned to China in 1997.
It is now part of China under a "one country, two systems" principle, which ensures that it keeps its own judicial independence, its own legislature and economic system.
But people in Hong Kong are worried that should the extradition bill pass, it would bring Hong Kong more decisively under China's control.
Hong Kong officials have said Hong Kong courts will have the final say whether to grant extradition requests.
Ms Lam's government has also said suspects accused of political and religious crimes will not be extradited, insisting legally binding human rights safeguards will also be in place.