Self-governed Taiwan is China's most sensitive issue and is claimed by Beijing as its sacred territory. President Xi Jinping has stepped up pressure on the democratic island since Tsai, from the pro-independence Democratic Progressive Party, became president in 2016.
Taiwan is only one of a growing number of flashpoints in the US-China relationship, including a trade war between the countries, US sanctions on the Chinese military, and China's increasingly muscular military posture in the South China Sea.
Tsai's comments came days after Chinese President Xi Jinping said nobody could change the fact that Taiwan was part of China, and that people on both sides of the Taiwan Strait should seek "reunification".
The Tax & Legal Reform League, an activist group, called the protest after marshaling about 20,000 people outside the presidential office in an initial demonstration a week before this, and another 10,000, according to organizers and Taiwanese media.
The results will be closely watched in China, which claims self-ruled and proudly democratic Taiwan as its own and which has ramped up pressure on President Tsai Ing-wen and her administration since taking office in 2016.
Taiwan officials say the population of 23 million is regularly fed misleading information in the news media and on social networks that range from unverified footage of large-scale Chinese military drills to false reports of stranded travelers being abandoned by the island’s government.
El Salvador and the Dominican Republic are among a growing number of countries that have cut ties with Taiwan in favour of establishing relations with China, which considers the self-governing island democracy to be part of its territory.
It was not clear whether the system, called automatic train protection, had switched off by itself or had been manually disabled before the accident on Sunday, the head of a government-led investigation team Wu Ze-cheng said.