Tsai condemned Xi's comments and rejected the Chinese President's "one country, two systems" proposal, telling reporters in Taipei: "We hope that the global community takes it seriously and can voice support and help us".
According to news reported by Reuters, in Taipei, Tsai said, "We hope that the global community takes it seriously and can voice support and help us", giving reference to Xi's threat to use several forces to bring the country under its control.
If the worldwide community did not support a democratic country that was under threat, "We might have to ask which country might be next?".
After his win, Cho said the party would carry out the 2020 presidential nomination race in accordance with the DPP's mechanism, and all party members were equally eligible, the Liberty Times reported. He beat polling specialist You Ying-lung, who has been critical of the president.
In 2016, Ms Tsai and the DPP secured a landslide election victory, sweeping away a government that had built much closer ties with China over the previous decade.
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It is hoped that the changes to the law will mean that women are no longer be kept in the dark about their marital status. "The male guardianship system is a core issue and it must be dismantled".
Tsai resigned the party chairmanship but stayed on as president, staying above the fray in the vote to replace her. The speech comes after Taiwanese President Tsai Ing-wen asked the PRC to respect Taiwan's sovereignty.
Following Chinese President Xi Jinping's speech on January 3 threatening to "reclaim" Taiwan by any means necessary, Tsai responded defiantly in a Facebook post the same day, reiterating that Taiwan has never and will never accept the "1992 Consensus", nor the "one country, two systems" arrangement proposed by Beijing.
Voting began Sunday morning, with preliminary results expected to be announced in the evening.
J. Michael Cole, a Taipei-based expert with the University of Nottingham's China Policy Institute, said the vote bolstered Tsai's chances of standing for a second term.
"A chairman who is at odds with Tsai will definitely be a minus [for the party]", he said.
The U.S. remains Taiwan's most powerful military ally but maintains the stance that Taipei must not move close to a formal declaration of independence for fear of stoking a Chinese invasion.