The cars used sophisticated software to evade U.S. emission rules.
The bill would raise the bar for plaintiffs to join a class action, requiring each of them to have "suffered the same type and scope of injury."
"Our emissions testing will in future be verified by internal and external third parties."
More Volkswagen, Audi and Porsche owners could face recalls of their cars.
The auto giant admitted to a cheating on a CO2 emissions test, too.
The troubled carmaker suspects the camshaft lobe may shear off reducing engine and brake power.