Winterkorn, who recently saw off a challenge to his leadership with the ousting of long-time chairman Ferdinand Piech, has built Volkswagen into a global powerhouse since he took the helm in 2007, with brands ranging from budget Seats and Skodas to premium Audis and top-end Porsches and Lamborghinis.
But he has also faced criticism for a centralised management style which some analysts say has hampered the company's efforts to address long-standing underperformance in North America.
"I am sure that there will be personnel consequences in the end, there is no question about it," supervisory board member Olaf Lies told German radio station Deutschlandfunk on Tuesday.
Workers in Wolfsburg, where Volkswagen employs over 50,000 people, were angry about the damage to the company's image. "If Winterkorn knew of the manipulation, then he must go," said one staffer who works at the plant's human resources department.
Late on Monday, Volkswagen's US chief Michael Horn said the company had "totally screwed up" and promised to make amends.
At 1240 GMT, Volkswagen shares were down 20.1 percent at 105.7 euros after touching a low of 101.35 euros.
Shares in rivals including Peugeot, Renault and Fiat Chrysler also fell sharply amid signs regulators across the world will step up scrutiny of vehicle tests, which environmentalists have long criticised for exaggerating fuel-saving and emissions results.
"No doubt we will hear a lot from plaintiffs' attorneys representing the poor car buyers but I guess the group that would have been hurt most would have been the other car manufacturers who compete with Volkswagen," said one Swiss based hedge fund manager, speaking on condition of anonymity.
The EPA said on Monday it would widen its investigation to other automakers, and French Finance Minister Michel Sapin said on Tuesday an EU-wide inquiry was needed too.
"It has to be done at a European level," he told Europe 1 radio. "We are a European market with European rules. It is these that have to be respected. It is these that have been violated in the United States."
There have been no suggestions so far that other carmakers have engaged in the same practices as Volkswagen. German rivals BMW and Daimler have said the accusations against Volkswagen did not apply to them.
The European Commission said it was in contact with Volkswagen and US authorities, and that it was premature to say whether any specific checks on the carmaker's vehicles were needed.
Switzerland and Italy said they would separately investigate Volkswagen's diesel vehicle emissions tests.
South Korea's environment ministry also said it would investigate 4,000 to 5,000 of Volkswagen's Jetta, Golf and Audi A3 vehicles produced in 2014 and 2015, and could expand its probe to all German diesel cars if it found problems.
German auto supplier Bosch said on Tuesday it had supplied the components to Volkswagen that are now at the centre of the US probe into test rigging.
"We produce the components after specification of Volkswagen," it said in an e-mailed statement. "The responsibility for application and integration of the components lies with Volkswagen."
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