Volkswagen said Tuesday that some 11 million diesel vehicles worldwide were fitted with software at the center of the U.S. emissions scandal.
It said it was setting aside around 6.5 billion euros ($7.3 billion) to deal with service costs and other expenses and hoped "to win back the trust of our customers."
Volkswagen said in a statement that it was "working intensely to eliminate these deviations through technical measures."
Volkswagen -- which faces stiff penalties for rigging its diesel cars to pass U.S. air pollution tests -- got a more immediate smack on Monday, losing more than $17 billion, or nearly a quarter of its market value.
List of Volkswagen cars recalled
Shares of the German car manufacturer closed at a more than three-year low in Frankfurt, a day after Martin Winterkorn, Volkswagen's chief executive, apologized, saying the company would cooperate with U.S. agencies and would also conduct an internal probe.
CBS News has learned the U.S. Justice Department is conducting a criminal probe of Volkswagen's conduct in what could test the department's promise to hold individuals accountable for corporate criminal conduct.
While the EPA has said Volkswagen faces up to $18 billion in fines, Klaus Breitenbach, an analyst at Baader Helvea Equity Research, told CBS MoneyWatch he believes the penalties ultimately assessed will be below that figure, and the greater hit will be to the company's reputation.
"Why would you do this is another question," Breitenbach said. On the face of it, Volkswagen made a large gamble for relatively small stakes, given the company's U.S. sales account for only 6 percent of its global volume, and of the roughly 600,000 cars sold in the U.S. last year, just 120,000 to 150,000 were diesel.
One attorney now involved in litigation against Volkswagen likens the case to Hyundai Motor America and Kia Motors America, which in late 2013 agreed to pay $400 million for inflating the fuel economy claims for their vehicles.
The Associated Press contributed to this report.