Those who wish to push for Taiwan's independence risk overturning the "boat of peace" and must be stopped, the main newspaper of China's ruling Communist Party said on Sunday, a day after a historic meeting between China and Taiwan's leaders.

Meeting in Singapore on Saturday, China's President Xi Jinping told Taiwan's president they must not let proponents of Taiwan's independence split them, at the first get-together of leaders of the two sides since China's civil war ended in 1949.

Ma Ying-jeou, president of self-ruled, democratic Taiwan, where anti-Beijing sentiment has been rising ahead of elections, called for mutual respect for each other's systems and said Taiwan people were concerned about mainland missiles pointing their way.

Taiwan's opposition Democratic Progressive Party (DPP), which has traditionally favored the island's independence, is the frontrunner to win the presidential polls, something Beijing is desperate to avoid happening.

Only the people of Taiwan can decide its future and will do so in elections in January, the island's opposition leader and presidential frontrunner said on Sunday.

Tsai Ing-wen, leader of Taiwan's independence-leaning Democratic Progressive Party (DPP), said the leaders' meeting had done nothing to make Taiwan's people feel safer.

"Only the majority public opinion on Jan. 16 can decide Taiwan's future and cross-strait relations," Tsai wrote, referring to ties with the mainland.

China views self-ruled and proudly democratic Taiwan as a renegade province, to be bought under its control by force if necessary, and has warned that moves towards formal independence could stoke conflict.

In a commentary, the Communist Party's official People's Daily said the two leaders sitting together showed a desire not to let the "tragedy of history" repeat itself nor to let the fruits of peaceful development be lost.

Progress over the past seven years - referring to the rule of the China-friendly Ma - has been possible due to a joint political will to oppose Taiwan independence and accept there is "one China", albeit it with different interpretations, the paper said.

"If this 'magic cudgel' did not exist, the boat of peace would encounter a fierce and frightening storm, or even flip over completely," it wrote.

"Compatriots on both sides of the Taiwan Strait must join together and resolutely oppose the Taiwan independence forces and their separatist activities," the newspaper added.

China's Nationalists, also known as the Kuomintang (KMT), retreated to Taiwan after losing the civil war to the Communists, who are still in charge in Beijing.

The Communists and Nationalists both agree there is "one China" but agree to disagree on the interpretation.

While bilateral trade, investment and tourism have blossomed - particularly since Ma and his KMT took power in 2008 - there is deep suspicion on both sides and no progress has been made on any sort of political settlement.

Several hundred people took to the streets of Taipei on Saturday to protest against the meeting.