The demonstrations are expected to be the biggest since the 2014 Umbrella Movement, which also saw hundreds of thousands take to the streets.
Yu said the extraction bill, which is used by the Chinese government as a frightening tool to achieve the effect of authoritarian rule, has a two-pronged effect on Taiwan.
"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. No one would be extradited if they face political or religious persecution or torture, or the death penalty, they say.
The bill has caused political gridlock, outcry among the city's usually pro-conservative business community, and even physical scuffles in the city's legislature, as well as criticism of the Hong Kong government by the United States and European Union.
Chris Patten, the last British governor of Hong Kong, said on Thursday the bill would "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".
Dense crowds chanting "Scrap the evil law!" and "Oppose China extradition!" stretched for miles.
She also mentioned that if the bill is passed, the U.S.is very likely to suspend Hong Kong's status as an independent tariff region, further causing distress to China's economy. "That has an impact on my future".
Protestors gathered at the Hong Kong Economic and Trade Office, from where they marched to the Consulate General of People's Republic of China at 240 St. George Street. They fan for each other, help push the wheelchairs.
"If Hong Kong people are not standing out (to protest) and get the law passed, the woe will pass on to our kids and their kids", he told Reuters in Cantonese.More news: Modi woos Sri Lanka, Maldives as India fends off Chinese influence
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Lo said he had last attended a protest in 2003, when half a million Hong Kongers rallied against national security legislation - a common refrain from many of Sunday's protesters.
But the proposal has gridlocked the city's Legislative Council, which is roughly divided between pro-democratic and pro-Beijing camps.
Hong Kong's leaders say the law is needed to plug loopholes and stop the city from being a bolthole for mainland fugitives.
Supporters of the law have said Hong Kong courts will have the final say over whether to grant such requests, and suspects accused of political and religious crimes will not be sent to mainland China for a trial.
Image copyright EPA Image caption Hong Kong and China - one country, two systems Why the change now?
Officials initially seized on the murder previous year of a young Hong Kong woman holidaying in Taiwan to justify swift changes.
Reuters reported earlier that several senior Hong Kong judges were anxious about the changes, noting a lack of trust in mainland courts as well as the limited nature of extradition hearings.
"The procession today is an example of Hong Kong people exercising their freedom of expression within their rights as enshrined in the Basic Law and the Hong Kong Bill of Rights Ordinance".
The former British colony was handed back to Chinese rule in 1997 amid guarantees of autonomy and various freedoms including a separate legal system, which many diplomats and business leaders believe is the city's strongest remaining asset.
The city has its own laws and its residents enjoy civil liberties unavailable to their mainland counterparts. "We have no enough power to resist as Hong Kong government is supported by the mainland", said Lai, who suffers from Parkinson's disease.