Almost half of the Volkswagen cars in Europe affected by the diesel emissions scandal require major hardware changes – including the installation of new parts – in order to meet pollution standards.

The revelation by the German transport ministry that 3.6m cars in Europe require hardware changes underlines the scale and expense of the repairs that will be required as a result of the scandal.

Michael Horn, the boss of VW in America, told a congressional hearing on Thursday that the hardware fix was “complex” and could involve a new fuel injector tank being fitted to cars.

Horn insisted the performance of the car should not be affected by the repairs but revealed that Volkswagen was considering offering full refunds to customers who did not want their car back.

VW has admitted that 11m vehicles worldwide, including 8m in Europe and 1.2m in the UK, were fitted with defeat devices that allowed them to cheat emissions tests. The carmaker has put aside €6.5bn (£4.8bn) to meet the cost of recalling the cars and commercial vehicles, but it also faces the threat of fines of up to $18bn (£11.7bn) from the US and potential legal claims from shareholders and motorists.

The defeat device is a line of software code hidden within the cars’ systems that recognised when it was being tested. Some of the vehicles involved in the scandal can be fixed by rewriting the code. However, others will require more significant repairs. These hardware changes could include changing the catalytic converters and injector systems in the car, as well as installing a new tank.

The German transport ministry said 3.6m vehicles with 1.6-litre engines would require hardware changes. It is unclear at this stage if cars with other engines will also need the hardware repairs.

VW has released few details about its plan to recall the cars. However, Matthias Müller, chief executive of VW, said it would begin early in 2016.