By Jessie Pang and Aleksander Solum

HONG KONG, June 4 (Reuters) - Thousands gathered in Hong Kong on Tuesday for a candlight vigil to mark the 30th anniversary of the highly sensitive crackdown in Beijing when Chinese troops opened fire on student-led democracy protesters in and around Tiananmen Square.

Demonstrators sat peacefully in the financial hub's Victoria Park, holding up candles, placards and rallying next to a replica of the Goddess of Democracy statue which was erected in Tiananmen Square during the 1989 demonstrations in Beijing.

"It is very important that Hong Kong people continue to remember the June 4 tragedy, and indeed, preserve the memory," said Richard Tsoi, vice-chairman of the Hong Kong Alliance in Support of Patriotic Democratic Movements of China.

"And don't let the Chinese authority try to erase the memory for the whole nation."

The anniversary remains taboo in China, which has never provided a death toll for the 1989 violence. Rights groups and witnesses say it could run into the thousands.

In Beijing on Tuesday, hundreds of uniformed and plainclothes police monitored the square and its surroundings, conducting spot ID checks and inspecting car trunks.

In comparison, the anniversary draws thousands every year in Hong Kong, which returned to Beijing's rule in 1997 under a "one country, two systems formula" that guarantees rights and freedoms not seen on the mainland.

The vigil in the financial hub is the biggest on Chinese soil. Smaller vigils are held in the former Portuguese territory of Macau and the self-ruled island of Taiwan, which China claims as its own.

Ahead of the anniversary, censors at Chinese internet companies say tools to detect and block content related to the 1989 crackdown have reached unprecedented levels of accuracy, aided by machine learning and voice and image recognition.

While the June 4 vigil is an annual event in Hong Kong, it comes at a sensitive time for the city's leaders this year as they grapple with a backlash at home and abroad over a proposed extradition bill that would for the first time allow fugitives captured in the city to be sent to mainland China for trial.

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Critics of the bill plan to protest in Hong Kong on Sunday, with rally organizers calling for 300,000 people to take to the streets.

"I will definitely also join the big protest on Sunday," said chef Kevin Mok, 22.

"I know that I must stand out, for our freedom, for our safety, for Hong Kong's economy."

Others chanted "Oppose the extradition law" as they urged people to join the rally on Sunday.

Some curious mainland Chinese were among the crowds.

"I hope the government never covers up the truth any more," said Trance, 21, a university student from mainland China. "There is a wall between us and the world outside of the mainland."

Beijing has increased government suppression of rights activism, pushing the 1989 demonstrators' original goals further away than ever.

On Thursday, China's Defence Ministry took exception to the use of the word "suppression" to refer to how the military put down the Tiananmen protests, and said China had made great strides.

(Reporting By Aleksander Solum, Jessie Pang, James Pomfret; Writing by Anne Marie Roantree, Editing by Nick Macfie)