Carmakers pledged such incentives last week in a deal with German officials to overhaul software in more than 5 million diesel cars to try to avert a ban on diesel fuelled vehicles after the emissions cheating scandal.

Rebates announced on Tuesday across the VW (>> Volkswagen) group range from 2,000 to 10,000 euros at the core VW brand, 3,000 euros to 10,000 euros at its luxury division Audi (>> Audi AG) and 5,000 euros at sportscar maker Porsche.

BMW (>> Bayerische Motoren Werke), Daimler (>> Daimler) and Ford (>> Ford Motor Company) have also offered incentives to switch to newer, cleaner cars.

The VW incentives are valid to the end of the year and its customers can gain additional discounts of 1,000 to 2,380 euros for buying alternative energy cars including electric, hybrid and natural gas-powered vehicles, VW said.

VW's emissions test cheating - exposed by U.S. regulators almost two years ago - led to wider revelations that diesel vehicles from most manufacturers release far more toxic nitrogen oxides (NOx) on the road than in laboratory tests.

With possible driving bans looming in several major German cities and federal elections due next month, carmakers will be hard pressed to clean up diesel models, of which VW says there are 6.4 million on Germany's roads, to meet new Euro-4 and older European Union emissions standards.

"We cannot count on the state to help us in this phase," VW sales chief Juergen Stackmann said on a call.

(Reporting by Andreas Cremer; Editing by Edward Taylor and Alexander Smith)