Hyundai's affiliate Kia Motors Corp, also being sued for overstating the fuel economy of some models, is evaluating whether to join the settlement, according to the filing.
Both companies are facing lawsuits after announcing in early November that they overstated the fuel economy performance on more than 1 million recently sold vehicles by at least one mile per gallon.
A settlement amount was not disclosed. Hyundai offered a lump sum payment option as part of its settlement proposal.
Lawyers for Hyundai and the plaintiff drivers said they plan to file more details on the settlement with the court. A hearing to discuss the accord and how to implement it is scheduled for Thursday morning.
The companies' admission came after a probe by the US Environmental Protection Agency, which found errors in the mileage ratings of 13 Hyundai and Kia models from 2011 to 2013 model years.
Both companies agreed to compensate owners for the added fuel costs. Under the plan, customers will receive a debit card that will reimburse them for the difference in fuel economy, plus an extra 15% to acknowledge the inconvenience.
The news was a blow to Hyundai and Kia, both of which bragged about their vehicles' superior fuel economy in advertisements. Hyundai's "4 x 40" strategy centered on offering four models that got 40 mpg, including the Elantra small car.
Hyundai said in Tuesday's court filing that it would offer a lump sum option to drivers in lieu of its reimbursement plan.
Current drivers who bought one of the four Hyundai models that claimed to get 40 mpg will get a higher lump sum payment compensation, according to Hyundai's proposed settlement. Those models include the Accent compact car, the hybrid version of the Sonata sedan and the Veloster small car.