FRANKFURT, Germany — Volkswagen has agreed to pay at least $1.2 billion in buybacks and compensation to settle claims from U.S. owners of cars with larger diesel engines that the company rigged to cheat on emissions tests.

And the German automaker could pay even more — as much as $4 billion — if it can’t repair many of the cars in a way that satisfies regulators.

The proposed settlement filed late Tuesday covers owners of some 78,000 Audi, Volkswagen and Porsche cars with 3.0-liter diesel engines.

Volkswagen has already agreed on a $15 billion settlement for some 500,000 smaller, 2.0-liter diesel engines.

With the settlements for both small and large engines, “all of our customers with affected vehicles in the United States will have a resolution available to them,” Hinrich Woebcken, head of Volkswagen Group of America, said in a statement. “We will continue to work to earn back the trust of all our stakeholders.”

Under Tuesday’s proposed class action settlement, owners of 20,000 older models dating back to 2009-2012, which cannot be fixed to meet pollution standards, will be offered buybacks or trade-ins. In addition, they will be paid compensation ranging from $7,755 to $13,880, according to a statement from owners’ attorneys.

People who bought 58,000 newer cars from model years 2013-16, which can be fixed, will get compensation of $7,039 to $16,114. Volkswagen says those cars can be made to comply with pollution limits, while older models cannot.

VW’s proposed repair must win approval from U.S. environmental authorities by an agreed deadline. If not, buybacks could push the cost as high as the $4.04 billion laid out in court documents.