The U.S. Environmental Protection Agency (EPA) alleged on Friday that the automaker had used software to trick regulators measuring toxic emissions on its diesel vehicles between 2008 and 2015. The software allowed the cars to emit pollutants above legal limits pollutants while on the road, but reduced the pollution during emissions tests.
Volkswagen said on Sunday that it had launched an investigation. In a statement, chief executive Martin Winterkorn said: "I personally am deeply sorry that we have broken the trust of our customers."
A video posted to the Volkswagen's website on Tuesday showed Winterkorn apologizing again and pledging to work on uncovering the full extent of the company's actions.
"I am endlessly sorry that we betrayed the trust" of millions of people, Winterkorn said, adding that "swift and comprehensive clarification has now utmost priority."
"To make it very clear: Manipulation at VW must never happen again," he added.
Volkswagen shares plunged 18 percent on Monday and nearly 20 percent on Tuesday on the back of the admission, as German government officials expressed concern that the scandal could damage the reputation of its car industry.
On Tuesday, Olaf Lies, a German politician who also sits on Volkswagen's supervisory board, told radio station Deutschlandfunk that he expected heads to roll at the company once it is clear who was responsible for falsifying the U.S. tests.
"I am sure that there will be personnel consequences in the end, there is no question about it," Lies said.
Read MoreVolkswagen stock drops 20% on US diesel recall probe
The U.S. Department of Justice, meanwhile, has reportedly begun a criminal probe into Volkswagen's actions. And lawmakers on the House of Representatives' Oversight and Investigations Subcommittee said they would hold a hearing on the issue in the coming weeks.
The cheating could see Volkswagen face U.S. penalties of up to $18 billion.
On Tuesday South Korea's environment ministry said it planned to conduct an investigation into emissions from Volkswagen and Audi diesel cars, in response to the U.S. revelations.
In Australia, a spokesman for the Department of Infrastructure and Regional Development said: "The department is seeking urgent clarification from Volkswagen Group Australia, as to whether vehicles supplied to the Australian market use similar software to that used in the U.S."
An official from Taiwan's Environmental Protection Administration told CNBC it was concerned about the scandal and would ask Volkswagen's local plant for a report on its cars. The official added that the ministry would closely monitor the German government's decision on how to deal with Volkswagen.
—Reuters contributed to this report.
Correction: Michael Horn was speaking at the launch of the 2016 Passat. An earlier version misstated the year.