Authorities in the US have reportedly approved a fix for around 38,000 vehicles fitted with the Volkswagen Group 3.0-litre TDI turbo-diesel engine as part of the Dieselgate emissions scandal.

According to reports from the United States, a letter made public earlier this week says VW Group brands have been approved to make hardware and software changes to vehicles fitted with the 3.0-litre TDI engine, which has previously been confirmed to have emissions-cheating devices on board.

The 2013-16 model-year Volkswagen Touareg and Porsche Cayenne, along with the 2013-15 model-year Audi Q7 are included in this campaign.

This could reportedly save VW more than US$1 billion ($1.28 billion), as it no longer has to buy back affected models. Back in May, a court order stated that the German manufacturer would have to buy back the 'dirty' vehicles if it couldn't devise a government-approved fix.

However, Volkswagen did agree to spend over US$1.22 billion ($1.56 billion) to fix or buy back 80,000 vehicles with 3.0-litre turbo-diesel engines in the US, with owners to receive between US$8500 and US$17,000 ($10,877-$21,754) if they choose to obtain a fix rather than sell their vehicle back to the company.

Autoblog says the total cost could have risen to around US$4.04 billion ($5.17 billion) if the US Environmental Protection Agency (EPA) and California Air Resources Board failed to approve fixes for the affected 3.0 TDI models.

This news comes after Greenpeace protesters boarded a ship delivering diesel Volkswagens to protest the German manufacturer (above), while removing the keys to several thousand vehicles awaiting distribution to suppliers in a Kent holding yard last month.

Closer to home, Porsche has announced it will undertake a voluntary recall of its Cayenne SUV fitted with the 3.0-litre V6 diesel, affecting around 2100 units in Australia. Read the full story here.

The diesel emissions saga has cost the Volkswagen Group billions in fines and lawsuits, while key staff have also been prosecuted for their involvement. As part of its recovery, Volkswagen announced its plans to be the world's leading electric vehicle (EV) manufacturer, projecting annual sales of 3 million units globally across its brands by 2025.