TAIPEI--Taiwan said it would opt in while Japan and Canada stayed on the sidelines as a deadline passed Tuesday for joining a China-led development bank, though signals from Taiwanese officials that Taipei would set conditions on its membership status raised possible complications for a final agreement.

Taiwan is among a number of U.S. allies that have said they want to join the Asian Infrastructure Investment Bank--an international development bank designed to finance road, rail, port and other construction projects--despite concerns from Washington about its governance and transparency.

The AIIB is seen as critical to China's efforts to use economic development to place itself at the center of a new Asian order. Washington sees it as a potential rival to the World Bank and other institutions where the U.S. holds greater sway.

The U.K., Germany and France also are seeking AIIB membership.

Fresh from meetings with top Chinese officials in Beijing, U.S. Treasury Secretary Jacob Lew criticized the pace of Beijing's economic overhauls Tuesday but was more conciliatory on the AIIB, saying that the U.S. welcomed the bank. "I was encouraged by my conversations in Beijing in which China's leaders made clear that they aspire to meet high standards and welcome partnership," Mr. Lew said in a speech to the Asia Society Northern California.

Japan indicated it would let pass Tuesday's deadline for applying to become a founding member of AIIB, though it didn't rule out joining later. Canada said Tuesday it was still considering whether to participate.

Though Taipei said it would apply to join, some Taiwanese officials indicated its membership name could be an issue. Taiwan officials said they had submitted a letter of intent to join the bank to Chinese authorities, using simply the name "Taiwan." It wasn't clear what name Taiwan would use when filing a formal application for membership, or whether Chinese officials would stick to that name.

In a statement, China's Taiwan Affairs office said it received the letter and didn't see a problem with Taiwanese membership, depending on the name. "The AIIB is open and accommodating, and we welcome Taiwan's participation with an appropriate name."

Earlier Tuesday, Premier Mao Chi-kuo told lawmakers that Taiwan would rather not join the AIIB if Taiwan isn't respected or doesn't enjoy the same rights as other members.

"Our [membership] name has to be reviewed and accepted by all our people, " Mr. Mao said. "Our bottom line is the ones that are already widely used internationally."

Nomenclature is a sensitive issue in Taiwan. Under pressure from China, which sees Taiwan as a renegade province, the island of 23 million people has been competing in international sporting events as "Chinese Taipei" and joined the World Trade Organization as "the Separate Customs Territory of Taiwan, Penghu, Kinmen and Matsu."

In 1986, after China joined the Asian Development Bank, the institution changed Taiwan's membership name to "Taipei, China," from "Chinese Taipei." The change met with protest from Taiwan's government, which said the name suggested Taiwan was under China's jurisdiction. But the change went into effect, and Taiwan is still a member of the ADB.

Tuesday night, dozens of protesters scuffled with police outside the Presidential Office building. Protesters said President Ma Ying-jeou, who announced the plan, didn't consult the public on it and has denigrated Taiwan's sovereignty by submitting the letter of intent.

Taiwan's government has internally discussed joining the AIIB since January, the presidential office said Tuesday. Officials including the central bank governor and finance minister in recent weeks have publicly backed the move, saying it would foster the island's international profile and economic development, while Taiwan's businesses would benefit from increased infrastructure spending in the region.

On the sidelines of the regional Boao Forum in China's Hainan province last week, Vincent Siew, Taiwan's former vice president, expressed the island's intent to join the AIIB during a closed-door meeting with Chinese President Xi Jinping, Taiwan's official China News Agency reported Sunday.

Chen Deming, China's top negotiator with Taiwan, told reporters at Boao that Beijing "does not see any difficulty" in Taiwan joining the institution.

Some observers said Beijing could exert more influence over Taiwan through the institution, on top of other cross-Strait trade agreements signed over the past few years.

"The AIIB is a China-centric institution and China undoubtedly will try to exert its power over Taiwan through it. But since the operation of the bank remains opaque, for now we have no idea how to quantify that impact," said Hao Pei-chih, a public-policy professor at National Taipei University in Taiwan.

Chen Chien-jen, Taiwan's former foreign minister, was more sanguine about the move. "There are dozens of founding members and China probably cannot exert too much control over the bank just by itself."

Cross-Strait relations have warmed since 2008, as President Ma has supported dozens of trade agreements with China, Taiwan's biggest export destination. But defeats for Mr. Ma's party, the ruling Kuomintang, in local elections late last year have complicated such ties.

Fanny Liu in Taipei and Lilian Lin in Beijing contributed to this article

Write to Aries Poon at aries.poon@wsj.com

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