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Volkswagen has agreed to pay at least $1.2bn (£1bn) to fix or buy back 78,000 diesel cars in the US to settle more emissions-cheating claims.

Without regulatory approval, the German car giant could be forced to buy back all of the cars, costing it about $4bn.

And the deal, another in its long-running emissions scandal, still needs approval from the courts.

Car components company Robert Bosch, a VW supplier, has also agreed to pay $327.5m to US owners of affected cars.

The proposed settlements for the three-litre cars are the last major US hurdle for VW over its emissions scandal.

VW previously agreed to spend up to $10bn to compensate the owners of about 482,000 two-litre vehicles after it admitted it had installed secret software to disguise emissions.

The on Wednesday that US customers who bought the three-litre diesel cars would be fully compensated "through a combination of repairs, additional monetary compensation, and buybacks for certain models".

Owners of 2009 to 2012 models could get between $26,000 to $58,000 for a buyback, depending on the model, mileage, and trim of the car, the FTC said.

For owners and people leasing 2013 to 2016 models, Volkswagen is expected to get regulatory approval for a fix that makes the cars compliant with US environmental regulations, the FTC added.

However, if VW fails to get Environmental Protection Agency and the California Air Resources Board approval for the modification within a certain time frame, it must offer to buy back those vehicles, upping the amount it has to pay to about $4bn.

Analysis: Theo Leggett, 91�ȱ� News business reporter

This is the latest in a series of settlements reached by Volkswagen with the US authorities.

It has already agreed to pay $10bn to compensate around 482,000 people who bought cars with two-litre diesel engines that had been fitted with defeat devices. That included the cost of repairing or buying back affected vehicles. At the same time, it agreed to spend $4.7bn on schemes to offset excess emissions and develop clean vehicles.

Thursday's $1.2bn VW settlement extends the compensation offer to cover owners of vehicles with larger three-litre engines - sold under the VW, Audi and Porsche brands.

And on top of all that, in January the company agreed to pay $4.3bn in civil and criminal fines to the US authorities.

All of which takes the total bill for the scandal in the US alone to more than £20bn.

The company's drive to provide "clean diesel" technology to the American market has been a very expensive disaster. Nevertheless, assuming the most recent settlements are approved by the courts, VW will probably be happy to have got the bulk of its US litigation out of the way.

And as for its reputation - it may have been tarnished, but the company still managed to sell 10.3 million cars last year - more than any other major manufacturer. Car buyers, it seems, have pretty short memories.

VW's US chief executive Hinrich Woebcken said: "With the court-approved two-litre TDI programme well under way and now this proposed three-litre TDI programme, all of our customers with affected vehicles in the US will have a resolution available to them.

"We will continue to work to earn back the trust of all our stakeholders and thank our customers and dealers for their continued patience as this process moves forward."

Bosch said in a statement it didn't admit wrongdoing or accept liability but had decided to settle so it could focus on an extensive "transformation process" the company has embarked on.

A federal judge in San Francisco will hold a 14 February hearing on whether to grant preliminary approval for the settlements.