TAIPEI, Sept 19 (Reuters) - The number of mainland Chinese visiting once-forbidden Taiwan after a landmark tourism agreement is way below the island's expectations due to China's strict travel rules, an official said on Friday.

"The problem of the degree of China's screening process is causing the number of people to fall below expectations," Corinna Wei, spokeswoman for the island government's Mainland Affairs Council, told Reuters.

China rigorously screens citizens for proof they intend to return from the relatively well-off Taiwan after their tours, contributing to a tourist headcount that has averaged several hundred people per day, not the legal maximum of 3,000 per day.

Taiwan President Ma Ying-jeou spearheaded the 3,000-person daily maximum, enough he said to boost the island's service sector, one of the hardest-hit parts of an economy beset by inflation, wage stagnation and unemployment.

China requires each Taiwan-bound traveller to prove employment or pay 50,000 yuan (S$10,400), in addition to providing other forms, to qualify for trips.

"This month the number (of visits) hasn't been ideal," Ma said at a news conference on Thursday. "Mainland China's management of tourists is pretty strict."

China has claimed sovereignty over Taiwan since 1949, when Mao Zedong's Communists won the Chinese civil war and Chiang Kai-shek's Nationalists (KMT) fled to the island. Beijing has vowed to bring Taiwan under its rule, by force if necessary.

But in June the two sides signed an agreement to launch direct Friday-through-Monday charter flights and to allow China tourists visit once-forbidden Taiwan. Previously, Chinese were rarely allowed to visit Taiwan, due to security concerns.

(Reporting by Ralph Jennings; Editing by Valerie Lee)