Many of those taking part carried yellow umbrellas, recalling Hong Kong's massive 2014 pro-democracy protests, the leaders of whom have been sentenced to up to 16 months in prison.
Hong Kong police said around 22,800 people took part in Sunday's protest at its peak period.
Revisions to the law would make it easier to send criminal suspects to mainland China, where they could face vague national security charges and unfair trials.
"Hong Kong and China have completely different legal systems," said marcher Roland Lo, 49.
"Creating a loophole that could mean a Hong Kong person gets extradited to China to face prosecution there, that completely destroys the guarantee of human rights and legal protection of one country, two systems."
Under that system, Hong Kong was guaranteed the right to retain its own social, legal and political systems for 50 years following its handover from British to Chinese rule in 1997.
Another marcher, Amanda Wong, 40, said it was important to exercise those rights while they were under perceived attack.
"We have to come out to march. It doesn't matter if we can change the situation or not, we just have come out while we still have the chance," she said.
Business, legal, human rights and journalists groups have expressed concerns over the proposed changes, saying they will damage Hong Kong's reputation for legal independence.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)