According to Audi, these engines will gain new software for free, which will "further improve their emissions in real driving conditions beyond the current legal requirements".
The luxury car maker says this move will ensure the "future viability of diesel engines" and "make a contribution towards improving air quality". It also hoping to stave off moves by certain jurisdictions, such as Paris, which are planning to ban the use of diesel engines.
As part of Audi's on-going Dieselgate investigations, it has been "intensively examining all diesel concepts for any irregularities" for several months, and since 2016 "all engine and transmission combinations have been systematically reviewed".
The company claims it has been working closely and reporting to the German Federal Ministry of Transport and the Federal Motor Transport Authority.
German government's investigations have yet to be concluded, but if they "result in further consequences, Audi will of course quickly implement the required technical solutions in the interest of its customers as part of this EU5/EU6 retrofit program".
Earlier this week, Mercedes-Benz announced it would voluntarily recall around three million vehicles with Euro 5 and Euro 6 diesel engines.
We're waiting to hear back from Audi Australia about whether the voluntary recall involves Australia.