A senior administration official told the Financial Times that the British decision was taken after "virtually no consultation with the U.S." and at a time when the G-7 had been discussing how to approach the new bank.
"We are wary about a trend toward constant accommodation of China, which is not the best way to engage a rising power," the U.S. official said.
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British officials were publicly restrained in criticizing China over its handling of Hong Kong's pro-democracy protests while Mr Cameron has made it clear he has no further plans to meet the Dalai Lama, Tibet's spiritual leader — following a 2012 meeting that prompted a furious response from Beijing.
While Beijing has long been suspicious about U.S. influence over the World Bank and IMF, China also believes that the U.S. and Japan have too much control over the Manila-based Asian Development Bank. In addition to the AIIB, China is the driving force behind the creation last year of the Brics development bank and is promoting a $40 billion Silk Road Fund to finance economic integration with Central Asia.
The Obama administration has said it is not opposed to the AIIB, but U.S. officials fear it could become an instrument of Chinese foreign policy if Beijing ends up having veto power over the bank's decisions.
The U.K. Treasury denied that Britain had acted out of the blue, saying there had been "at least a month of extensive consultation" at a G-7 level, including with Jack Lew, U.S. Treasury secretary.
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George Osborne, chancellor of the exchequer, was unrepentant, arguing that Britain should be in at the start of the new bank, ensuring that it operates in a transparent way. He believes it fills an important gap in providing finance for infrastructure for Asia.
"Joining the AIIB at the founding stage will create an unrivaled opportunity for the U.K. and Asia to invest and grow together," Mr Osborne said. He expects other western countries, which have been making positive noises privately about the new bank, to become involved.
Beijing launched the AIIB in October with the backing of 20 other countries, but Japan, South Korea and Australia — America's main allies in the region — did not become founding members. There has been a strong debate with the Australian cabinet about whether to join, after U.S. pressure to stay on the sidelines.
A decision by the major economies to join now would give up leverage they might have over the AIIB as it was being set up, the U.S. official said: "Large economies can have more influence by staying on the outside and trying to shape the standards it adopts than by getting on the inside at a time when they can have no confidence that China will not retain veto powers."