"The process of clarification and transparency must continue. This is the only way to win back trust. I am convinced that the Volkswagen Group and its team will overcome this grave crisis," Winterkorn said on Wednesday.
The board has yet to announce a successor to 68-year-old Winterkorn. However, rumors earlier suggested he might be replaced by Porsche CEO and President Matthias Muller, although Volkswagen has denied this.
As a result of the crisis, VW stock on Wednesday received a series of downgrades from the likes of Deutsche Bank and JPMorgan.
"We now rate VW Neutral (OW) with a new December 2016 target price of €179 (from €253), as we lack clarity on the potential total cost of the recall and the risk of additional engine investigations," JPMorgan wrote in a note on Wednesday.
Meanwhile, Societe Generale downgraded the European automobile sector to "neutral" from "overweight." Nonetheless, most auto stocks finished trade in the green, with the exception of France's Peugeot Citroen and Renault, which both closed down over 2 percent.