DETROIT — Volkswagen is offering $1,000 in gift cards and vouchers as a goodwill gesture to owners of small diesel-powered cars involved in an emissions cheating scandal.

The offer announced Monday goes to owners of 482,000 cars in the U.S., many of whom are angry at the company because they paid extra for the cars to be environmentally sensitive without losing peppy acceleration.

VW is working on a fix for the cars, which are equipped with software that turns on pollution controls during government tests and turns them off while on the road. The U.S. Environmental Protection Agency says the cars, with 2-liter four-cylinder diesel engines, emit 10 to 40 times the allowable amount of harmful nitrogen oxide while being driven.

The offer also includes free roadside assistance for the diesel vehicles for three years.

VW said that its Audi brand would launch the same program on Friday.