BEIJING/TAIPEI (Reuters) - China welcomes Taiwan's decision to apply to join the Beijing-led Asian Infrastructure Investment Bank (AIIB) as long as the self-ruled island uses an appropriate name, state news agency Xinhua reported on Wednesday.

China's Taiwan Affairs Office has received Taiwan's letter of intent to join and has passed it to the AIIB's interim secretariat, Xinhua cited Taiwan Affairs Office spokesman Ma Xiaoguang as saying.

"The AIIB is open and inclusive," Ma said. "We welcome Taiwan to participate in the AIIB under an appropriate name."

Most countries, including the United States, do not recognise Taiwan due to pressure from China. Taiwan is not a member of the United Nations, the World Bank or the International Monetary Fund.

However it is a member of the Asian Development Bank under the name of Taipei, China.

China views Taiwan as a renegade province and has not ruled out the use of force to bring it under its control. However, since Taiwan's current president Ma Ying-jeou took office in 2008, enmity has declined considerably and the two sides have signed a number of trade and investment deals.

The AIIB issue has touched off a heated debate in Taiwan since the Presidential Office announced the island's intent to join on Monday.

The government says the move will help Taiwan in its efforts for regional economic integration and raises the possibility of it joining other multinational bodies.

"We also want to join under an appropriate name. If the name is not appropriate we will not join," Taiwan Premier Mao Chi-kuo said on Wednesday.

Critics are concerned though that Taiwan will be not be allowed to join the multilateral investment bank as an equal member and are worried about closer cross-strait ties.

Late on Tuesday a small group of protesters of mainly young Taiwanese gathered in front of the Presidential Office accusing President Ma of "selling out Taiwan" in its bid to join the AIIB.

"This issue has caused strong dissatisfaction among the people," said the Democratic Progressive Party, the main pro-independence opposition party.

The United States has urged countries to think twice about joining the AIIB until it could show sufficient standards of governance and environmental and social safeguards.

(Reporting by Ben Blanchard and J.R. Wu in TAIPEI; Editing by Raju Gopalakrishnan and Rachel Armstrong)