China last month dashed the island's hopes of becoming a founding member of the Asian Infrastructure Investment Bank (AIIB), though a Chinese foreign ministry spokesman said at the time it could join under an "appropriate name".
The issue was raised as Zhang, director of China's Taiwan affairs office, met Andrew Hsia, chairman of Taiwan's top China policy decision-making body, the Mainland Affairs Council, in Kinmen -- a Taiwan-administered island off China's Xiamen city.
China and Taiwan split at the end of the civil war in 1949 when the Kuomintang fled the mainland after a defeat at the hands of the Chinese Communist Party. But Beijing still regards the island as a province awaiting reunification.
As a result, China routinely opposes moves by Taiwan to join international organisations, arguing it is not a country.
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Earlier this month, the head of Taiwan's ruling Kuomintang party (KMT) Eric Chu said he remained "optimistic" about joining the bank and proposed joining under the name "Chinese Taipei".
In his opening speech, Hsia hailed the significance of the meeting at Kinmen, which was the scene of a fierce 44-day bombardment by the Chinese army beginning on August 23, 1958, which killed 618 servicemen and civilians and injuring more than 2,600.