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“This is not a political thing; this is something that every other country does,” Mr. Bloomberg said in an interview with the television network he founded. “If we’re going to be competitive, we have to do it.”

The National Association of Manufacturers, which is urging lawmakers to reauthorize the bank, said nearly 90 percent of the transactions support small businesses and that the bank operates at no cost to taxpayers.

Mr. Obama also is facing questions about whether his position has shifted on the issue of corporate “inversions,” in which U.S. corporations adopt foreign addresses to avoid taxes. The president has called the firms “corporate deserters,” and the administration is considering steps that would limit those companies from maximizing their tax breaks.

Mr. Obama said at a news conference Wednesday night that his administration wants to move “as quickly as possible” to close the tax loophole. He acknowledged that Treasury Secretary Jack Lew said previously that the administration couldn’t solve the problem.

“We don’t want to see this trend grow,” Mr. Obama said. “It’s not fair, it’s not right. We’re reviewing all of our options.”

But Bloomberg News reported Wednesday that during the auto bailout in 2009, the Treasury Department authorized spending $1.7 billion to keep afloat a bankrupt Michigan auto parts manufacturer. The company, Delphi Automotive, then moved its paper headquarters to England, potentially reducing its U.S. tax by up to $110 million per year.

Delphi recently disclosed in a Securities and Exchange Commission filing that it received a “notice of proposed adjustment” from the Internal Revenue Service, asserting that the agency believes Delphi should be treated as a domestic corporation for federal income tax purposes, retroactive to Oct. 6, 2009.

A wave of U.S. companies is seeking to change to foreign addresses to avoid the U.S. corporate tax rate of 35 percent, the highest in the developed world.

Treasury Department spokesman Adam Hodge said former Treasury officials “have said they were not involved in Delphi’s decision to incorporate overseas or in any decision Delphi made regarding the tax implications of the company’s emergence from bankruptcy.”