The federal motor vehicle office (KBA) told VW to set out "binding measures and a timetable" by the deadline showing how it will meet emissions standards without resorting to software that rigs test results, Bild am Sonntag reported.
If Volkswagen fails to meet the deadline, the KBA warned in a two-page letter, the authority could withdraw approval for the affected models, meaning they could no longer be sold or even moved on German roads.
The German industrial titan sparked global outrage when it admitted that 11 million of its diesel cars, including 2.8 million in Germany, are fitted with so-called defeat devices that activate pollution controls during tests but covertly turn them off when the car is being driven.
Bild am Sonntag also reported that German auto parts supplier Bosch had produced the controversial software but had warned the VW Group as early as 2007 that it was meant for test use only and that using it on the road would be illegal.
The biggest scandal in VW's history has badly tarnished its name, left it exposed to billions in fines in the United States and investigations in countries from Norway to India, as well as wiping about a third off its stock market value in a week and forcing a leadership change.
The embattled carmaker on Friday tapped Matthias Mueller -- the 62-year-old chief of the VW Group's luxury sports car brand Porsche -- to steer the world's largest automaker by sales out of the crisis.
A Volkswagen spokesman told AFP the company would soon present an action plan in Germany and "announce when we expect to launch a recall" that would include a software update.
"We are working at full throttle" on the plan, the spokesman said.
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