"Our continued failure to approve the IMF quota and governance reforms is causing other countries, including some of our allies, to question our commitment to the IMF and other multilateral institutions that we worked to create and that advance important US and global economic and security interests," the Financial Times quoted Lew as saying.
"Our international credibility and influence are being threatened," he added.
Lew's warning came as Italy, France and Germany followed UK's lead and announced on Tuesday their intention to join the China-backed Asian Infrastructure Investment Bank (AIIB) as founding members, despite Washington's concerns that the bank is a potential competitor of the US-based IMF and World Bank.
AIIB is an international financial institution proposed by China. The purpose of the multilateral development bank is to provide finance to infrastructure projects in the Asia-Pacific region.
The bill establishing the bank was signed by 21 countries in October 2014, including Singapore, Malaysia and Kazakhstan among others.
Earlier in the day, Luxembourg's Finance Ministry confirmed to Sputnik news agency the country's bid to become a member of the Asian Infrastructure Investment Bank.
The new investment bank will be headquartered in Beijing. March 31 is the deadline for accepting founder-members.