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.

But some analysts have been skeptical that Mr. Müller is the right person to steer the company through its current troubles. Before heading Porsche, Mr. Müller was Volkswagen’s head of product planning from 2007 to 2010, a period when many of the cars that caused the scandal were being developed.

He was also a longtime lieutenant to Martin Winterkorn, the chief executive who resigned in September after regulators in the United States first disclosed that the automaker had installed defeat software on some diesel models. In day-to-day usage, with the mandatory controls turned off, the cars showed better engine performance but emitted as much as 40 times the legal limits of nitrogen oxide, a pollutant linked to lung ailments.

The new revelations escalate the potential damage to Volkswagen’s finances and reputation. Audi and Porsche are the source of most of the company’s earnings, because profit margins tend to be higher on luxury cars. In contrast to Volkswagen brand cars, which have struggled in the United States, Audi and Porsche are success stories in North America, which is the biggest market for Porsche.

The E.P.A.’s report opens a new chapter in its investigation of Volkswagen’s deceitful practice. The new devices were uncovered after investigators said on Sept. 25 that they would test all diesel car models, a week after disclosing Volkswagen’s fraud. The tests were performed by E.P.A., the California Air Resources Board and the regulatory group Environment Canada.

“VW has once again failed its obligation to comply with the law that protects clean air for all Americans,” Cynthia Giles, the assistant administrator for E.P.A.’s Office of Enforcement and Compliance Assurance, said in a statement.

Regulators have not found similar defeat devices on diesel models produced by other automakers. Testing is continuing, and the agency plans to make its final results public.

Hours after the E.P.A. made its latest accusations, Volkswagen disputed the findings. “Volkswagen AG wishes to emphasize that no software has been installed in the 3-liter V6 diesel power units to alter emissions characteristics in a forbidden manner,” Volkswagen’s statement read.

But in a six-page letter explaining its findings, the E.P.A. described in detail a mechanism it says was set up to intentionally beat emissions testing. It said the devices were not described in the vehicles’ certification application and were set up to defeat a federal emission test procedure known as FTP 75.

The agency said the new tests found that Volkswagen had installed the devices in some Volkswagen, Audi and Porsche diesel cars with 3.0-liter engines, encompassing model years 2014 through 2016.

The notice described how once the vehicle’s electronic brain detected the cars were being tested, it would direct the car to operate emission control parameters — including injection timing, exhaust gas recirculation rate and fuel pressure — to reduce nitrogen oxide emissions. Once back in normal driving conditions, the car would increase the release of nitrogen oxide up to nine times the agency’s standard.

Asked about Volkswagen’s statement challenging the E.P.A.’s claims, a spokeswoman for the agency reiterated that the undisclosed existence and use of devices meant to circumvent emission controls was illegal under the Clean Air Act.

The latest finding covers about 10,000 passenger cars already sold in the United States since the model year 2014. The violation notice also covers an unspecified number of 2016 vehicles. The cars found to have the software installed are the diesel versions of the 2014 VW Touareg, the 2015 Porsche Cayenne and the 2016 Audi A6 Quattro, A7 Quattro, A8, A8L and Q5.

In a separate notice from California’s Air Resources Board, which also has broad authority to regulate emissions, regulators there backed the findings from the E.P.A. “ARB is very disappointed with this development as VW (along with all the other manufacturers) was alerted on September 25, 2015, that A.R.B. would be immediately conducting defeat device testing,” the California regulator said in its notice to Volkswagen.

Until now, investigators in the United States and Europe had focused on 2.0-liter engines and smaller models. Volkswagen has admitted that more than 11 million cars were equipped with this fraudulent software, including 482,000 in the United States.

The latest development has left many observers stunned. Congressional investigators indicated they would continue pressuring VW for answers.

“The latest revelations raise the question, where does VW’s road of deceit end?” senior leaders of the House Energy and Commerce Committee said in a joint statement. “It’s time for Volkswagen to fully come clean.”

Drew Kodjak, executive director of the International Council on Clean Transportation, an environmental group whose testing played a role in revealing the VW scandal, said the E.P.A.’s findings “confirm that Volkswagen made a tremendous mistake in its corporate risk assessment, believing it could get away with this type of cheating and believing the repercussions would be modest.”

The company, one of Germany’s largest, is facing investigations in Europe and in the United States. It has already set aside 6.7 billion euros, about $7.4 billion, to cover the expense of recalling and repairing cars equipped with the illegal software, though by some estimates the scandal is likely to cost Volkswagen considerably more than that.

Volkswagen has suspended several high-ranking officials. Its shares have lost 36 percent of their value since the fraud was disclosed by E.P.A. on Sept. 18. During the first nine months of this year, Audi generated operating profit of €4 billion, or about 40 percent of the Volkswagen total. Porsche generated €2.6 billion.

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