Former MP Cheng Li-wun, who will take over as leader of the Kuomintang (KMT) party on November 1, won Saturday's election at a time of rising tension with Beijing, which views the democratically governed island as its own territory. Taiwan's government strongly objects to China's sovereignty claims.
The KMT traditionally backs close relations with China and is Beijing's preferred dialogue partner. China refuses to talk to Taiwan President Lai Ching-te and his Democratic Progressive Party (DPP) administration, calling him a "separatist".
Xi, in a message in his role as head of China's Communist Party on Sunday, told Cheng the two parties should strengthen their "common political foundation", the official Xinhua news agency reported.
Both parties should also "unite the vast majority of people in Taiwan to deepen exchanges and cooperation, boost common development, and advance national reunification," he added.
Cheng, in her message to Xi, did not make any mention of union with Beijing, but said both sides of the Taiwan Strait were "members of the Chinese nation", using an expression in Chinese that refers to ethnicity rather than nationality.
"Both parties should, in light of the current situation, strengthen cross-Strait exchanges and cooperation on the existing foundation (and) promote peace and stability across the Taiwan Strait," Cheng said, according to a party statement.
While the KMT lost the presidential election last year, the party and its ally, the small Taiwan People's Party, together hold the most seats in parliament.
Cheng, 55, opposes Taiwan increasing defence spending, a key policy plank of Lai's, and won the leadership vote over the KMT establishment candidate, former Taipei mayor Hau Lung-bin.
Accusations of Chinese interference in the election by a key supporter of Hau's, the KMT's vice presidential candidate last year, Jaw Shau-kong, overshadowed the campaign. Jaw said social media accounts had spread disinformation about Hau.
China said on Wednesday that the election was a KMT matter, and that online comments did not represent an official stance.
Writing on his Facebook account on Sunday, Jaw said the KMT must reduce pro-China influence and that the majority of Taiwanese desire peaceful relations and dialogue with China.
"The KMT must recognise that elections are held in Taiwan, and voters are in Taiwan, not mainland China," Jaw added.
Late on Saturday, DPP spokesperson Justin Wu said there were clear signs of Chinese interference in the KMT election, comments they dismissed.
