The government has never released a full death toll, but estimates from human rights groups and witnesses range from several hundred to several thousand.
The government of democratically-ruled and Chinese-claimed Taiwan, in a statement on the anniversary's eve, said Beijing was avoiding saying sorry for what had happened or reflecting on its mistakes.
"We express regret, and call on the other side to implement people-centred political reforms, stop suppressing people's democratic demands, and return power to the people as soon as possible," it said.
China's Taiwan Affairs Office did not immediately respond to a request for comment.
China claims Taiwan as its own territory, to be taken by force if necessary.
The coronavirus pandemic has worsened already poor ties between Taiwan and China. Taiwan says China has been trying to block its access to vaccines, while China says Taiwan is playing politics with people's lives by refusing shots from China.
On Friday, activists will mark the Tiananmen anniversary with at least one public event in Taipei, although much scaled down from previous years due to a spike in COVID-19 cases on the island.