The previous accusations, which affected mostly Volkswagen vehicles but also some Audi and Porsche cars, involved only diesel models sold from 2009 to 2015.

The California Air Resources Board is taking the lead in testing Audis in the United States, according to the lawsuit. The agency, which also did much of the detective work to expose cheating with Volkswagen’s diesel models, said it could not comment on a pending investigation. The Kraftfahrt-Bundesamt, which is responsible for enforcing emissions standards in Germany, did not reply to a request for comment.

The revelations came a week after Volkswagen disclosed that the chairman of its supervisory board, Hans Dieter Pötsch, was under investigation for violating German securities laws in connection with the emissions fraud.

If it turns out that more cars had illegal software known as “defeat devices,” Volkswagen could face even more criticism that it remains in denial, is still run by the many of the same people who were in charge while the wrongdoing was taking place and is unable to contain the damage to the carmaker’s finances and reputation.

Mr. Pötsch was the longtime chief financial officer at Volkswagen before becoming supervisory board chairman in October. He is suspected of failing to notify shareholders quickly enough of the financial risks of the diesel emissions cheating scandal.

An internal company document from 2013, a copy of which was obtained by The New York Times, offers clues to the origin of the software believed to be used in concealing the true carbon dioxide emissions of the Audi vehicles. The document, reported by the German newspaper Bild am Sonntag, recorded the outcome of test drives of new vehicles in southern Africa in February 2013. It was standard procedure at Volkswagen to test new vehicles in South Africa and Namibia, where top executives critiqued performance and ordered changes.