Volkswagen has reached a deal with the United States government to buy back or fix nearly 500,000 diesel cars in the country rigged to cheat emissions tests, and will create an additional $1 billion (£698 million) fund to compensate owners. The "deal in principle" outlines the basic parameters of the settlement, but details on exactly how much consumers with different cars will be paid remains to be worked out,Associated Press (AP)reports.

The agreement is expected to be announced in San Francisco at a federal court hearing on Thursday 21 April — though the deal won't include a specific payout plan.

Depending on model, year and the engine type of cars, some owners will have the option of choosing a buy back, or a repair of their car — though Volkswagen reportedly hasn't yet come up with a way to fix the cars that currently spew nitrogen oxide at 40 times the maximum limit allowed.

The German car manufacturer is expected to offer to buy back up to 500,000 2.0-litre diesel vehicles sold in the US that exceeded allowable emission levels, sources tell Reuters. Those cars would reportedly include versions of the Jetta sedan, the Golf compact and the Audi A3 sold since 2009. The buyback offer will not apply to the bigger, 80,000 3.0-litre diesel vehicles, which also exceed pollution limits, including Audi and Porsche SUV models, the sources said.

As part of the settlement with the US, including the Environmental Protection Agency (EPA), Volkswagen has also agreed to provide the $1bn compensation fund for owners, another source told Reuters.

The fund will be in addition to the cost of buying back the vehicles, but it is not clear how much each owner might receive, the person said.

"They've agreed on a maximum amount of money" for compensation, a source told AP. "How it's allocated and distributed, that remains to be seen."

If divided equally among all the car owners, the compensation fund would amount to only $1,700 (£1,200) a consumer. Owners of newer models get a software fix and little money. Some 325,000 owners of older cars requiring more extensive repairs likely will get more.

Owners are expected to have up to two years to decide whether to sell back vehicles or get them repaired. It is not clear whether VW will be allowed to resell vehicles they buy back, sources told Reuters.

At the San Francisco hearing where the settlement is expected to be revealed senior US district court judge Charles Breyer will likely also discuss a schedule for depositions and information exchange between the parties. If he's not satisfied with the agreement, he could set a trial date.

Neither VW nor federal authorities commented on the reported agreement.