BEIJING/HONG KONG (Reuters) - Security was tight and access restricted to Beijing's Tiananmen Square on Tuesday, the 35th anniversary of the June 4 crackdown, while Hong Kong also increased policing as activists in Taiwan and elsewhere prepared to mark the date with vigils.

Chinese tanks rolled into the square before dawn on June 4, 1989, to end weeks of student and worker protests.

Decades after the military crackdown, rights activists say the demonstrators' original goals - including a free press and freedom of speech - remain distant, and June 4 is still a taboo topic in China.

The ruling Communist Party has never released a death toll, though rights groups and witnesses say the figure could run into the thousands.

Taiwan's president Lai Ching-te said in a statement on Tuesday that "the memory of June 4th will not disappear in the torrent of history".

Lai, who was inaugurated last month as the leader of the democratic island China claims as its own, added that Taiwan would "respond to authoritarianism with freedom."

In Beijing, an official website for the Tiananmen Tower overlooking the square, posted a notice earlier saying it would be closed for the entire day on June 4, and that those who had bought tickets could get them refunded.

The official social media account of the Beijing subway network announced that an exit of Tiananmen East station would be closed from June 2 to 5.

Small groups of "stability maintenance" volunteers - retirees with red armbands - have been keeping watch at neighbourhoods in central Beijing since last week. Guards have also been stationed on pedestrian bridges, a regular practice during politically sensitive periods.

On Chinese social media platforms including WeChat and Douyin, users were unable to change their profile photos, according to online posts and Reuters tests.

"Thirty-five years have passed, and the authorities remain silent. All that can be seen on the internet is 'A Concise History of the Communist Party of China', which says that a tragic incident was caused by the student movement in 1989," wrote the Tiananmen Mothers, a group of mostly China-based survivors and families of the victims of the Tiananmen crackdown.

"We cannot accept or tolerate such statements that ignore the facts."

In China-ruled Hong Kong, police officers tightened security around downtown Victoria Park, where large June 4 candlelight vigils had earlier been held annually before tougher new national security laws came into force in recent years.

Performance artist Sanmu Chen was taken away on Monday night by police as he attempted a mime performance near a police van. Chen was later released.

Last Tuesday, Hong Kong police arrested six people for sedition under a new national security law enacted this year, stemming from what media said were online posts linked to June 4. Two more have been arrested since.

(This story has been corrected to clarify that the Tiananmen Tower was closed to public, not the entire square itself, in paragraph 7)

(Reporting by Yimou Lee in Taipei, Laurie Chen in Beijing and Jessie Pang in Hong Kong; writing by James Pomfret; Editing by Lincoln Feast.)

By Laurie Chen and Jessie Pang