BBC News

The premium car brand, part of Volkswagen, said it “accepts the fine and… admits its responsibility”.

In June, VW agreed a €1bn settlement in Germany over the emissions scandal, which came to light in 2015.

Audi, whose ex-boss Rupert Stadler is being investigated over “dieselgate”, said affected cars spanned 2004-18.

Audi said in a statement that some V6 and V8 diesel engines were “placed on the market with an impermissible software function”.

In 2015, US investigators discovered that some VW diesel cars were fitted with what became known as “defeat devices” to flatter emissions readings during engine tests so that the true output of nitrogen oxides was reduced.

The scandal spread throughout the motor industry, engulfing not just VW and its other car brands, but to other motor manufacturers.

VW admitted in 2015 to putting defeat device software into 11 million cars worldwide. The company’s total costs in fines, buybacks and refits has now reached €27bn.

While the probe against Audi is now closed, other cases against executives from the VW group – including former chief executive Martin Winterkorn – remain open, with charges including fraud, false advertising and failure to keep investors informed.

Earlier this month, VW ousted Audi chief executive Rupert Stadler. In June, he was put under investigation by German prosecutors over alleged fraud and false advertising involving the sale of cars with defeat devices, and remains in police custody.

Audi’s fine of €800m consists of €5m for regulatory rule-breaking, with the rest payment for the economic benefits resulting from the sale of cars with defeat devices.

Audi, VW group’s most profitable brand, said the fine would hit its financial performance this year. The company’s share price initially fell on the news, but had recovered to stand 2% up by late morning.