The U.S. Export-Import (ExIm) Bank, which provides support to U.S. exporters and those that buy U.S. goods, is due to run out of money in June. It is targeted for closure by some Republicans in the U.S. Congress who believe the bank provides welfare for big business.
Read More Tea Party Divided by Export-Import Bank
Big U.S. firms such as GE and Boeing are beneficiaries of the Export-Import Bank.
"ExIm makes money, it contributes to small and medium-sized supplier development in the U.S.," Rice said. "I believe the U.S. should have participated in the Asian Infrastructure Investment Bank; that would have been a great opportunity to get in on the ground floor."
The $50 billion Asian Infrastructure Investment Bank (AIIB) set up by China last year is viewed as a rival to the Washington-based World Bank.
Read MoreAIIB gambit has US on edge
Former White House economic adviser, Larry Summers, wrote in a blog last month that the growing membership of the AIIB should be seen as a "salutary wake-up call" for the U.S. to become a better global citizen when it comes to economic co-operation.
Asked whether the problem lay with the U.S. administration or Congress, Rice said Congress was at fault here.
"I think there are a few people in Congress who believe in a world that speaks for small government and don't see the need for ExIm," he said.