FRANKFURT — Martin Winterkorn resigned as chief executive of Volkswagen on Wednesday, taking responsibility for an emissions cheating scandal that has gravely damaged the carmaker’s reputation.

“As C.E.O., I accept responsibility for the irregularities that have been found in diesel engines,” Mr. Winterkorn, 68, said in a statement.

But Mr. Winterkorn, who had run the company since 2007, continued to insist that he had personally committed no misconduct. “I am not aware of any wrongdoing on my part,” he said.

Less than a week earlier, the company admitted that some diesel cars in the United States were equipped with software built to fool emissions tests. And one day earlier, the chief issued a video apology in an attempt to salvage the situation, and perhaps his job. On Tuesday, Volkswagen said that 11 million cars worldwide contained the software, although the company did not clarify whether the software was also used to deceive regulators in other countries.