Volkswagen's chief executive said the company is "deeply sorry" and plans to fully cooperate with the U.S. Environmental Protection Agency in its investigation of the automaker's use of software to get around federal emissions regulations.

Volkswagen is taking the findings from EPA and the California Air Resources Board "very seriously," according to a statement from Martin Winterkorn, chief executive of Volkswagen AG.

"I personally am deeply sorry that we have broken the trust of our customers and the public." Winterkorn said. "We will cooperate fully with the responsible agencies with transparency and urgency to clearly, openly, and completely establish all of the facts of this case."

On Sept. 18, the EPA accused Audi and Volkswagen of using a software algorithm in its four-cylinder diesels to circumvent federal emissions standards. The cars from the 2009 to 2015 model years could detect when the car is undergoing official emissions testing and turn on full emissions controls only during that test. This would violate the Clean Air Act.

The allegations cover about 482,000 models, including the Jetta TDI, Beetle TDI, Golf TDI, and Audi A3 TDI. The Passat TDI is affected from the 2014-MY and 2015-MY.

Volkswagen has also ordered a separate external investigation into the matter.

"The trust of our customers and the public is and continues to be our most important asset," Winterkorn said. "We at Volkswagen will do everything that must be done in order to re-establish the trust that so many people have placed in us, and we will do everything necessary in order to reverse the damage this has caused. This matter has first priority for me, personally, and for our entire Board of Management."