The bill was fast-tracked through the city’s legislature. It is expected to receive a second reading on Wednesday.
Government officials hope it will win approval by the end of the June.
Despite widespread criticism from human rights groups, Hong Kong’s leader, Carrie Lam, moved forward with the legislation.
Opponents say they do not think China’s legal system would guarantee the same rights to defendants as they would have in semi-autonomous Hong Kong.
“What can we do to get Carrie Lam to listen to us, how many people have to come out to make her reconsider listening to the public?” Miu Wong, a 24-year-old office worker at the protests, told AP.
But Hong Kong’s leaders say there is a need for such law to close loopholes and stop the city from being a place of escape for mainland fugitives.
Hong Kong officials said critics and dissidents of the Chinese government under the new law would not be extradited.
Hong Kong is a former British colony that was returned to China in 1997. It kept the right to its own social, legal and political systems for 50 years under a “one country, two systems” framework.