China's President Xi Jinping Tuesday told a former vice president of Taiwan that Beijing respects the island's social system and lifestyle, state media reported, in a sign of the steadily improving relations between the two sides.

The meeting in Beijing between Xi and Lien Chan, also an honorary chairman of Taiwan's ruling Kuomintang (KMT) party, was the latest high-level encounter between the two sides, which split in 1949 after a civil war.

Mainland China has since been ruled by the Communist Party while capitalist Taiwan has adopted democracy.

Xi "said the Chinese mainland respects the social system and lifestyle that Taiwan compatriots have chosen," Xinhua news agency reported.

He noted that the Taiwanese have their own mentality due to the island's history, and said "we completely understand how Taiwan compatriots feel".

"Family affection will help heal past wounds and sincerity will help resolve existing problems," Xi said.

"It has never changed, and will never change that we belong to one nation," he said, according to Xinhua.

The four-day visit by Lien, who arrived Monday, follows the first government-to-government talks between Taiwan and China since they split 65 years ago after a civil war won by Mao Zedong's communists.

In an apparent nod to the political sensitivities of China-Taiwan encounters, Xinhua described Xi by his party title of "general secretary of the Communist Party of China Central Committee" rather than as state president.

Similarly Lien was described as "Kuomintang honorary chairman" and not as a former vice president of Taiwan, which Beijing still claims as part of its territory awaiting reunification.

Xi told Lien that both sides should work to remove obstacles to the peaceful development of relations.

"Regarding the long-existing political differences across the Taiwan Strait, we are willing to hold consultations with the Taiwan side on an equal basis under the One-China principle and make reasonable arrangements," Xi said.

"I believe that people on both sides have enough wisdom to figure out a solution," he said.

According to Taiwan's Central News Agency, Lien told reporters in Taipei Monday that he was not representing any organisation or political party, nor would he convey any message to Xi from Taiwan President Ma Ying-jeou.

Exactly a week ago, Wang Yu-chi, Taiwan's top official overseeing China policy, met his Chinese counterpart Zhang Zhijun in Nanjing, in a symbolic yet historic move between the former bitter rivals.

Lien became the first leader of the KMT, or Nationalist, party to visit China in 56 years when he met president Hu Jintao in 2005 to formally end hostilities with the Communists. Last year, Lien met Xi in Beijing.

Ties with China have improved markedly since Ma of the KMT -- which opposes Taiwanese independence -- became the island's president in 2008. He was re-elected in 2012 for a final four-year term.