Cheng Li-wun, chairwoman of Taiwan's largest opposition party, the Kuomintang (KMT), is in China on what she calls a peace mission to reduce tensions at a time when Beijing has stepped up military pressure against the island it claims as its territory.
Meeting in the Great Hall of the People in the first such encounter in more than a decade, Xi told Cheng that today's world is not entirely at peace, and peace is precious.
"Compatriots on both sides of the strait are all Chinese - people of one family who want peace, development, exchange, and co-operation," he said on Friday in comments carried by Taiwan television stations.
Both sides of the strait belong to "one China", Xi said, according to a separate state media read out.
"When the family is harmonious, all things will prosper," he said.
"Taiwan independence is the chief culprit in undermining peace in the Taiwan Strait - we will absolutely not tolerate or condone it."
Xi also mentioned the thorny subject of union between China and Taiwan, which has long been Beijing's goal but which Taiwan's government rejects.
"The KMT and Communist Party must consolidate political mutual trust, maintain positive interaction, unite compatriots on both sides of the strait, and join hands to create a bright future of the motherland's reunification and national rejuvenation," he said.
China refuses to talk to Taiwan President Lai Ching-te, saying he is a "separatist". Lai's administration has called on Cheng to tell China to stop its threats, and says Beijing should engage with the democratically elected government in Taipei.
Speaking to reporters in Taipei on Friday, Hsu Kuo-yung, general secretary of Taiwan's ruling Democratic Progressive Party, criticised the KMT for continuing to stall parliamentary approval for defence spending while Cheng is in China.
"Are you trying to give some kind of grand gift to Xi Jinping?" Hsu said.
The KMT once ruled all of China until the Republic of China government it led fled to Taiwan in 1949 after losing a civil war with Mao Zedong's communists, who founded the People's Republic of China.
No peace treaty or armistice has ever been signed and to this day neither government formally recognises the other.
Cheng told Xi that mutually beneficial cross-strait relations are what the public on both sides longs for, and that interactions and exchanges should be reciprocal.
"I, Li-wun, sincerely hope that one day in the future, I will have the opportunity to be the host and welcome General Secretary Xi and all of you here present in Taiwan," she added, using Xi's title as head of the communist party.
Cheng said she hoped that through the efforts of both parties, the Taiwan Strait will no longer be a focal point of potential conflict, and will certainly not become a "chessboard for outside forces to intervene in".
Both sides of the strait should further plan and build institutionalised and sustainable mechanisms for dialogue and cooperation, she added.
The US is Taiwan's most important international backer and arms supplier, despite a lack of formal diplomatic ties. Beijing has repeatedly demanded Washington stop arming Taipei.
The US has backed the Taiwan government's plans to increase defence spending.
