A logo of Volkswagen is seen at a dealership. Kim Hong-Ji/Reuters

Volkswagen Group of America CEO Michael Horn said Thursday that most of the company's diesel cars containing so-called defeat devices aimed at cheating emissions tests will require more than just a software patch. This means that for most owners of affected Volkswagen “clean diesel” cars, the fix will mean more than a quick visit to a dealer to remove the hidden programming code.

Speaking to a House subcommittee hearing, the German automaker’s top U.S. executive said 430,000 of the roughly 480,000 affected cars in the U.S. require a “major fix” to their exhaust systems.

“For those cars, a software-only solution will not be possible,” Horn said. “For those cars we are working on both software and hardware solutions.”

The news comes almost three weeks after Volkswagen AG admitted publicly to creating hidden software aimed at breaking U.S. emissions rules. About 11 million Volkswagen cars are affected worldwide, raising the ire of customers, dealers and regulators.

Out of the five affected models, the 2014 and 2015 model year Passat sedan is the only one that “most probably” can be fixed with a software patch, because it already has the necessary exhaust system components. The other diesel cars -- the Golf, the Jetta, the Beetle and the Audi A3 (all from the 2009 to 2015 model years) – will need mechanical work.

Horn said there is no timeline for the repairs required for these vehicles, and that Volkswagen has no plans to provide loaner vehicles because the U.S. Environmental Protection Agency considers the affected cars both legal and safe to drive.

The necessary hardware fix, which has yet to be worked out at the company’s Wolfsburg, Germany, headquarters, will exacerbate frustration among vehicle owners and probably amplify demands that Volkswagen buy back the cars for their original prices.

Horn also announced that Volkswagen would withdraw applications for government emissions certifications for its 2016 Passats, Jettas, Golfs and Beetles with diesel engines. An unknown number of these cars remain in quarantine at U.S. ports.

"The American people want to know why these devices were in place, how the decision was made to install them and how they went undetected for so long," Rep. Tim Murphy, R-Pa., chairman of the House Subcommittee of Oversight and Investigations, said in a statement before the hearings began Thursday. "We will get them those answers."

The Senate Finance Committee has opened a separate investigation over federal clean-vehicle tax credits Volkswagen gave to buyers of its Turbocharged Direct Injection “clean diesel” cars.