Shares in Volkswagen AG are sliding after the U.S. Justice Department sued the German automaker over emissions-cheating software fitted to diesel vehicles.

Volkswagen's shares were 3.1 percent lower at 122.45 euros ($133.05) in Frankfurt trading on Tuesday morning — easily the worst performer on the DAX index of blue chip stocks, which was 0.4 percent higher overall.

The Justice Department's move on Monday potentially exposes the company to billions in fines for clean air violations.

Volkswagen set aside 6.7 billion euros to deal with the costs of recalling and fixing cars after the scandal erupted in September, but the ultimate costs to the company are expected to be considerably higher. A raft of private class-action lawsuits filed by angry VW owners also is pending.