Some details were still being worked out on Tuesday by the parties, which include Volkswagen, the Environmental Protection Agency, the California Air Resources Board and the Justice Department.
“This settlement is about taking pollution out of the air we breathe,” said Cynthia Giles, the E.P.A.’s assistant administrator for enforcement and compliance assurance.
“It’s also about showing what a strong E.P.A. enforcement presence means for those who may break the law,” Ms. Giles said, highlighting the agency’s record of pursuing those who pollute illegally. Questions have been raised about how tough an enforcer the E.P.A. will be under the incoming Trump administration.
Altogether, Volkswagen’s civil settlements are the largest ever in the United States by an automobile company. The agreement in June included a $2.7 billion payment into an E.P.A. fund to offset the cars’ excess diesel emissions and an additional $2 billion investment in zero-emission vehicle projects.
The owners of the cars covered by the June agreement may also have their cars fixed, although regulators have yet to approve any fixes.
The latest settlement, for the 80,000 cars, is similar. But Volkswagen has told the government that it believes about 60,000 of them — the newer models — can be fixed to comply with federal emissions standards. If that remedy can be shown to work, Volkswagen will not have to buy back those newer cars, according to the consent decree.
The agreement “is another important step forward in our efforts to make things right for our customers,” Hinrich J. Woebcken, the president and chief executive of Volkswagen Group of America, said in a statement. He said the company was committed to resolving outstanding claims “as quickly as possible.”
Elizabeth Cabraser, the lead lawyer for the car owners, said lawyers were working to resolve remaining issues and had no further comment.
The estimated $1 billion cost to Volkswagen from Tuesday’s agreement assumes Volkswagen can fix the 60,000 cars. If it cannot and must buy them back, the company’s costs would soar because many are expensive luxury vehicles.
But an E.P.A. spokesman, Nick Conger, said a technical review and discussions with Volkswagen indicated that it was “very possible that the newer vehicles can be fixed to comply with the emission standards.”
The $1 billion figure also includes an additional $225 million payment that Volkswagen will make into the E.P.A. fund to offset the environmental effect of the excess emissions.
The settlements come at a challenging time for Volkswagen. On top of the scandal, Volkswagen is facing plunging sales in Brazil and Russia as those previously red-hot markets cool. Last month, the automaker said it would cut about 30,000 jobs worldwide under a plan meant to save $3.9 billion a year.
Volkswagen also stands to lose if President-elect Donald J. Trump follows through on plans to raise trade barriers with Mexico. Volkswagen opened a factory in the Mexican state of Puebla this year to serve the United States market.
Volkswagen still faces a criminal inquiry by the Justice Department and an investigation by attorneys general in 42 states, the District of Columbia and Puerto Rico. The automaker is also under investigation in a number of other countries, including South Korea, and back home in Germany, over its diesel cheating.
Volkswagen acknowledged last year that it had fitted 11 million cars worldwide with illegal software that made the vehicles capable of defeating pollution tests.
The cars detected when they were undergoing emissions testing and would turn on pollution-control systems, curbing toxic emissions at the cost of engine performance. But those emissions controls were not fully deployed on the road, where the company’s cars spewed nitrogen oxide at up to 40 times the levels allowed under the Clean Air Act.
The terms of Tuesday’s settlement could yet change. They require a review by Judge Breyer and must go through a period of public comment.
Volkswagen owners affected by the settlement are not bound by it, and some may decide to press for better terms or not to participate at all.