The Environmental Protection Agency said on Monday that it had discovered emissions-cheating software on more Volkswagen and Audi cars than previously disclosed and, for the first time, also found the illegal software in one of the carmaker’s high-end Porsche models.

The German carmaker disputed the claims, however, saying it had not installed defeat software on the models in question that would “alter emissions characteristics in a forbidden manner.” The company pledged in a short statement that it would cooperate with the E.P.A. “to clarify the matter in its entirety.”

The latest findings by environmental regulators put significant new pressure on Volkswagen and its new chief executive, Matthias Müller, who was previously the head of Volkswagen’s Porsche division. E.P.A. officials indicated the latest violations were found during testing performed by federal regulators and their counterparts in California and Canada. The implication is that Volkswagen did not provide the information.

Mr. Müller has vowed to investigate Volkswagen’s emissions scandal, in which millions of diesel cars were fitted with a “defeat device” that sensed when the car was being tested for emissions and activated pollution controls that, in normal driving, would remain inactive.