Activists have been protesting in Hong Kong since April when the Hong Kong government introduced the amendment bill.
A police spokesman said police estimated 240,000 were on the march "at its peak".
"It's a proposal, or a set of proposals, which strike a bad blow ... against the rule of law, against Hong Kong's stability and security, against Hong Kong's position as a great worldwide trading hub", the territory's last British governor, Chris Patten, said on Thursday.
Extradition is just the latest flashpoint in the city as Beijing has sought greater influence in recent years, attempting with varying degrees of success to exert control over Hong Kong's national security, education and electoral framework.
Protesters hold placards march in a rally against the proposed amendments to extradition law in Hong Kong, Sunday, June 9, 2019. The city's business and diplomatic communities have expressed concern that the bill could undermine the rule of law, while Sunday's march displayed widespread public opposition from a diverse cross-section of society, from pro-democratic political parties, to small business owners, to a network of housewives mobilized online.
Lam had yet to comment on the rally, which followed weeks of domestic discontent growing official concern from the U.S., European Union and foreign business lobbies that the changes would dent Hong Kong's vaunted rule of law and freedoms.
"It may be useless, no matter how many people are here. People really sense this is a turning point for Hong Kong".More news: Regulator proposes radical overhaul of "dysfunctional" bank overdraft charges
The organizers say more than 500,000 people showed up, with the protesters wearing all white and chanting "step down" and "shelve the evil law".
Some carried yellow umbrellas - a symbol of the pro-democracy Occupy protests that choked key city streets for 79 days in 2014.
"I come here to fight", said a wheelchair bound 78-year-old man, surnamed Lai, who was among the first to arrive at Victoria Park before the start of the march at 3pm.
"We know that China is very effective at crafting reasonably justified criminal offences against individuals who it views as being critical of the state", Hong Kong University law lecturer Sharron Fast said.
"We want to tell Carrie Lam that we don't want Hong Kong to become a Chinese city", one man yelled through a loudhailer, referring to Hong Kong's chief executive.
Alex Ng, a 67-year-old retiree, said he joined the protest because "I think that there was never any public consultation about this law, and there are a lot of uncertainties". "It could have significant implications for Hong Kong's reputation as one of the world's most important business hubs".
Sunday protests were also being planned in 25 cities globally, including London, Sydney, New York and Chicago.More news: French Open mission impossible for Thiem
However, people remain suspicious and question the fairness and transparency of the Chinese court system.
Chris Patten, the last British governor of Hong Kong, said on Thursday the bill would "strike a awful blow.against the rule of law, against Hong Kong's stability and security, against Hong Kong's position as a great global trading hub".
Foreign governments, including the US, have criticized the bill for fear it would impact Hong Kong's rule of law and financial markets, according to Reuters.
"Until the Chinese government is able to prove to us that its criminal justice system does not arbitrarily detain individuals, that there are fair and transparent judges, that the use of torture is not endemic... until all of these assurances are met, Hong Kong can not in good faith extradite individuals to China", Ms Fast said. "AmCham has serious reservations about the Hong Kong extradition bill", Tara Joseph, the president of AmCham in Hong Kong, told TIME.
They say the laws carry adequate safeguards, including the protection of independent local judges who will hear cases before any approval by the Hong Kong chief executive.
No-one will be extradited if they face political or religious persecution or torture, or the death penalty.More news: Explosion in Swedish town damages buildings, injures 25