"We know that we have let down customers, authorities, regulators and the general public here in America," the head of the German carmaker said at a media reception on the eve of the Detroit auto show.
"We are - I am - truly sorry for that and I would like to apologise once again for what went wrong at Volkswagen," he added, stressing that "our most important task in 2016 is to win back trust."
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"It's not only our cars we have to fix. We have to repair our credibility, too."
The Wolfsburg-based group admitted it installed software in around 11 million diesel cars of its Volkswagen, Audi, SEAT and Skoda brands worldwide that helped them evade emissions standards after US regulators discovered the problem.
The so-called defeat devices turn on pollution controls when the car is undergoing testing, and off when it is back on the road, allowing it to spew out harmful levels of nitrogen oxide.
The affair severely damaged Volkswagen's reputation and spawned a host of investigations in several countries.
The US government sued the carmaker for installing defeat devices on nearly 600,000 of its Volkswagen, Audi and Porsche vehicles sold in America between 2009 and 2015.
The complaint alleges that Volkswagen not only intentionally violated clean-air regulations but also obstructed the investigation by concealing facts and providing misleading information, despite the company's public pledges of cooperation.
Speaking to journalists after his speech, Mueller insisted that "we are not a criminal brand or group".
Volkswagen made "huge" technical mistakes, but had "no intention" to deceive the US public or regulators.
Civil penalties in the United States could run well above $20 billion. Volkswagen also faces a costly recall, and at least 650 class-action lawsuits from disgruntled US customers.
When asked about the fines, Mueller quipped that people "are overbidding each other every day" in their estimates.