DETROIT — Hyundai and Kia overstated the gas mileage on most of their models from the past three years in an embarrassing blunder that could bring sanctions from the U.S. government and millions of dollars in payments to car owners.

Because of the inflated mileage, discovered during an audit by the Environmental Protection Agency, the Korean automakers must retrofit the window stickers on the cars, reducing their fuel economy figures by one-to-six miles per gallon depending on the model, the agency said.

The EPA said its inquiry into the errors is continuing, and the agency would not comment when asked if the companies will be fined or if a criminal investigation is under way. But the EPA said it’s the first case in which erroneous test results were uncovered in a large number of vehicles from the same manufacturer. Only two similar errors have been discovered since 2000, and those involved single models.

Hyundai and Kia executives apologized for the errors, said they were unintentional, and promised to pay the owners of 900,000 cars and SUVs for the difference in mileage. The payments, which will be made annually for as long as people own their cars, are likely to cost the companies hundreds of millions of dollars.

The EPA said it received about a dozen complaints from consumers that the mileage of their 2012 Hyundai Elantra compact cars didn’t match the numbers on the window stickers. So staffers at the EPA’s vehicle and fuel emission laboratory in Ann Arbor, Mich., included the Elantra in an annual audit that focused on cars that lead their market segments in mileage.

The audit turned up discrepancies between agency test results and data turned in by Hyundai and Kia, the EPA said.