The government says the bill has built-in protections and will plug loopholes.
Organisers say there were one million protesters, which would make it the biggest march since the 1997 handover. Police say 240,000 were at their peak.
Hong Kong’s leader Carrie Lam has pushed for the amendments to be passed before July. Supporters say safeguards are in place to prevent anyone facing religious or political persecution from being extradited to mainland China.
But critics say those in the former British colony would be exposed to China’s deeply flawed justice system, and it would lead to further erosion of the city’s judicial independence.
Protesters, marching in the sweltering heat dressed in white, included a wide range of people – from businesspeople and lawyers to students, pro-democracy figures and religious groups. The march was mainly peaceful though pepper spray was used against some protesters.