The improper payments could be even higher since not all agencies reported to the Government Accountability Office.
The White House acknowledged that "the loss to the Federal Government is significant," but it pointed to a declining overall error rate: Just 3.5% from 5% in 2009.
"[T]he Administration, working together with the Congress, has significantly reduced improper payments," Beth Cobert, deputy director for management at the Office of Management and Budget, said in her testimony. "[W]e will continue to work closely with agencies to find the root causes of the improper payments."
The Department of Agriculture's School Breakfast program, which provides free or reduced-price meals to needy students -- had the highest error rate in 2013, at 25%.
Other programs with error rates above 15% include the Earned Income Tax Credit and the Small Business Administration's Disaster Assistance Loans program.
In congressional testimony Wednesday, government agencies said they have been working on better procedures and trying to recover improper payments already made.
The IRS said it is going to be challenging to make improvements, however, given its lack of adequate funding.
The agency says its 2014 budget of $11.29 billion is $850 million below the funding it received in 2010, despite the surging fraud and identity theft that is leading to many improper payments.
"I remain concerned about our ability to continue to make progress in all of these areas in light of our ongoing difficult budget environment," IRS commissioner John Koskinen said in his testimony.