Early on Wednesday protesters, some wearing face masks and helmets, blocked key roads around government buildings.
Police in riot gear responded by using pepper spray on protesters to disperse them and said they were prepared to use force.
The Legislative Council is set to debate the bill within hours.
Despite widespread opposition the government has said it will continue to push for extradition. A final vote is expected on 20 June where the pro-Beijing Legislative Council (LegCo) is expected to pass the bill.
In scenes resembling the 2014 pro-democracy Umbrella movement, thousands of protesters - mostly young people and students - have taken to the streets and attempted to block access to government buildings ahead of the debate.
"This behaviour has gone beyond the scope of peaceful gatherings," the Hong Kong Police Force said in a tweet on Wednesday.
"We call on [protesters] to leave as soon as possible... otherwise we will use appropriate force."
Critics of the bill of amendments to the extradition laws cite the alleged use of torture, arbitrary detentions and forced confessions in the Chinese judicial system.
The government has promised legally binding human rights safeguards and other measures it says should alleviate concerns.
Nevertheless, this has led to the largest rallies the territory has seen since it was handed back to China by the British in 1997.
Police said they are also investigating death threats made against Hong Kong's Chief Executive Carrie Lam and members of the justice department over the bill.