LOS ANGELES » Volkswagen has agreed to the ground rules of a plan to compensate drivers of nearly 500,000 diesel-engine vehicles that were rigged to cheat on emissions tests, a federal judge said today.

U.S. District Judge Charles Breyer said at a hearing in San Francisco that the automaker reached the broad outlines of a deal that would include buying back or fixing the cars to meet emissions standards, along with “substantial compensation” for car owners.

Details of the plan weren’t revealed, but the proposal applied to the 2-liter diesel vehicles involved in the case. VW also must deal with an additional 80,000 3-liter vehicles equipped with the faulty systems.

Breyer had given Volkswagen until Thursday to reach an agreement with the U.S. Environmental Protection Agency and the California Air Resources Board or face the prospect of a trial in his court this summer.

Some environmental groups took note of the lack of details and demanded that Volkswagen thoroughly resolve the issue.

“The final settlement needs to fix or remove all of the polluting cars still on the road, make whole the consumers who trusted the vehicles were lower-polluting and compensate for the pollution the faulty cars created,” Kathryn Phillips, director of the Sierra Club’s California chapter, said in a statement.

The EPA was represented in court by the Department of Justice, which said in a statement that “this agreement in principle addresses one important aspect of the department’s pending case against VW, namely what to do about the 2-liter diesel cars on the road and the environmental consequences resulting from their excess emissions.”

VW’s cheating, one of the worst scandals in automotive history, erupted in September when Volkswagen admitted that it had installed so-called cheat devices on diesel-powered cars from 2009 through 2015.

The devices allowed the vehicles’ engines to emit fewer pollutants during emissions tests than they would during normal road use. The cars include certain Jetta, Golf, Beetle and Passat models.

The scandal involved nearly 600,000 vehicles in the United States and 11 million Volkswagen vehicles worldwide.

Breyer is presiding over hundreds of class-action lawsuits filed against Volkswagen, which also faces possible fines and penalties levied by the EPA, the air resources board and other regulators.

Together with the proposed repairs and compensation for the VW car owners, the cost to Volkswagen could total billions of dollars.

Breyer gave the German automaker until June 21 to file the specifics of its plan.

Volkswagen issued a statement that did not include any details for providing its customers with relief, but the company said “these agreements in principle are an important step on the road to making things right.”

“As noted today in court, customers in the United States do not need to take any action at this time,” Volkswagen said, adding that it is “committed to earning back the trust of its customers, dealers, regulators and the American public.”

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©2016 Los Angeles Times