VW reached a settlement with US and California authorities to recall 83,000 diesel cars with 3-liter diesel engines, resolving the last major part of its emissions cheating scandal.

The agreement, involving VW, Audi and Porsche cars, is another step towards allowing Volkswagen to put the emissions cheating scandal behind it.

In June the German auto maker agreed to a $15 billion settlement for another 475,000 vehicles affected by the scandal.

The Environmental Protection Agency (EPA) estimates that the total cost of the 3-liter settlement, including buybacks, repairs, and environmental remediation, at about $1 billion.

VW reached a $14.7 billion settlement with 550,000 owners of smaller, 2-liter diesel cars in September.

About one-quarter of the affected owners will be able to sell their vehicles back to VW at a price yet to be determined. The other 60,000 vehicles will be repaired at no cost to their owners, becoming fully compliant with clean-air laws.

US District Judge Charles Breyer said owners of the 3-liter cars made between 2009 and 2016 would get “substantial compensation” for having them fixed or repaired.

However, there were some remaining issues to be resolved and another hearing will be held on December 22, he said.

VW spokeswoman Jeannine Ginivan said the deal was “another important step forward in our efforts to make things right for our customers”.

The company admitted in September 2015 to installing secret software in 475,000 US 2-liter diesel cars to cheat exhaust emissions tests and make them appear cleaner in testing than they really were. They emitted up to 40 times the legally allowable pollution levels.

The $15 billion settlement in June covered those vehicles, including an offer to buy them all back.

The US Justice Department said VW had agreed to contribute another $225 million to a fund to offset excess diesel emissions.

In a separate filing, California’s government said VW would increase the number of electric vehicles it sells in the state.

Robert Bosch, the German engineering company that made the software for the VW diesels, has also agreed in principle to settle civil allegations at a cost of about $300 million.