The decision by the three European governments comes after Britain announced last week that it would join the $50bn Asian Infrastructure Investment Bank, a potential rival to the Washington-based World Bank.

Australia, a key US ally in the Asia-Pacific region which had come under pressure from Washington to stay out of the new bank, has also said that it will now rethink that position.

The European decisions represent a significant setback for the Obama administration, which has argued that western countries could have more influence over the workings of the new bank if they stayed together on the outside and pushed for higher lending standards.

The AIIB, which was formally launched by Chinese President Xi Jinping last year, is one element of a broader Chinese push to create new financial and economic institutions that will increase its international influence. It has become a central issue in the growing contest between China and the US over who will define the economic and trade rules in Asia over the coming decades.

When Britain announced its decision to join the AIIB last week, the Obama administration told the Financial Times that it was part of a broader trend of “constant accommodation” by London of China. British officials were relatively restrained in their criticism of China over its handling of pro-democracy protests in Hong Kong last year.

Britain tried to gain “first mover advantage” last week by signing up to the fledgling Chinese-led bank before other G7 members. The UK government claimed it had to move quickly because of the impending May 7 general election. The move by George Osborne, the UK chancellor of the exchequer, won plaudits in Beijing.

Britain hopes to establish itself as the number one destination for Chinese investment and UK officials were unrepentant. One suggested that the White House criticism of Britain was a case of sour grapes: “They couldn’t have got congressional approval to join the AIIB, even if they wanted to.”

The US Treasury said on Monday night that it recognised the need for greater infrastructure investment around the world. However, it said any new institution should “incorporate the high standards that the international community has collectively built”, and that new members of the AIIB should “push for the adoption of these same high standards”.

Privately, US and Australian officials have suggested that the British decision to break ranks and join the bank was driven by commercial considerations and that London was blind to the broader geopolitical implications in the Asia-Pacific region.

South Korean media have reported that Seoul will also now rethink its decision not to join the AIIB. Japan, the US ally in the region that is most worried by China’s growing influence, is not expected to become a member.