FRANKFURT (Reuters) - Volkswagen has ordered an external investigation after U.S. regulators found software the carmaker designed for diesel cars gave false emissions data, its CEO said on Sunday, adding he was "deeply sorry" for the violation of U.S. rules.

"I personally am deeply sorry that we have broken the trust of our customers and the public," Martin Winterkorn said in a statement published by the carmaker on Sunday. "Volkswagen has ordered an external investigation of this matter."

The U.S. Environmental Protection Agency (EPA) said on Friday the software deceived regulators measuring toxic emissions, adding Volkswagen could face fines of up to $18 billion as a result.

"We do not and will not tolerate violations of any kind of our internal rules or of the law," Winterkorn said, adding the company was fully cooperating with the relevant agencies.

He gave no details on who would carry out the external investigation. 

Cynthia Giles, an enforcement officer at the EPA, said on Friday the cars in question "contained software that turns off emissions controls when driving normally and turns them on when the car is undergoing an emissions test".

The feature, which the EPA called a "defeat device", masks the true emissions only during testing and therefore when the cars are on the road they emit as much as 40 times the level of pollutants allowed under clean air rules meant to ensure public health is protected, Giles said. 

It affects 2009-2014 Jettas, Beetles, Audi A3s and Golfs and 2014-2015 Passats. 

(Reporting by Christoph Steitz; Editing by Mark Potter)