The IRS paid as much as $13.6 billion in bogus claims for the Earned Income Tax Credit last year, according to a report the agency’s internal auditor released Tuesday morning.

The Treasury Inspector General for Tax Administration said it warned the IRS in 2001 that it was making the erroneous payments, but two years later the agency hasn’t fixed the problem.

Over the last decade, the IRS could have paid out as much as $132.6 billion in improper payments.

“The IRS has made little improvement in reducing improper EITC payments as a whole since it has been required to report estimates of these payments to Congress,” the inspector general said. “The IRS acknowledges that further reductions in the EITC improper payment rate will be difficult to achieve.”

Investigators said the IRS is still violating an executive order President Obama signed in 2009 telling agencies to come up with ways to reduce improper payments.

The EITC is designed to transfer money to the working poor through the tax system. But analysts said it is a complex program that is difficult to check for eligibility.

Bogus payments can include those that never should have been paid, or were paid out in the wrong amount. According to the audit, the improper payments accounted for between 21 percent and 25 percent of all EITC claims in 2012. That means between $11.6 billion and $13.6 billion was misspent.

Those figures do show a little progress. In 2010, as much as 29 percent of EITC payments were erroneous, accounting for up to $18.4 billion.

In its response to the report, the IRS said it’s working with the White House Office of Management and Budget to try to reduce bogus payments.

“The IRS met with OMB on July 12, 2013, to discuss proposed supplemental measures,” Pamela J. LaRue, the IRS’s chief financial officer, wrote. “We will continue to work with them to finalize these measures and to obtain written concurrence that the IRS is meeting reporting expectations.”

Ms. LaRue said they acknowledged they were not in compliance with the executive order.