This isn't the first time VW's CEO has rejected calls to offer Europeans compensation. Earlier this year Müller spoke to Autocar at VW's annual meeting in the UK, stating that customers were unlikely to be offered a similar deal because the situation is very different on this side of the Atlantic.
"The overall situation differs between European countries and between the US and Europe," he said. "For instance, when we compare Europe with the US a complete carry over of what is under discussion in the US to the other parts of the world will not happen."
Müller explained that since the car maker's European emissions fixes shouldn't hinder performance, the situation was entirely different.
"It is our goal and so far we have stuck to this that the refitting of our vehicles will not lead to a lower performance or affect fuel consumption. That was our goal and so far we have been able to implement it."
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US owners might find themselves with reduced fuel economy after the fix is applied, however, so VW is offering to buy back diesel cars affected by the scandal there. It is also offering owners "substantial compensation" of $5000 each.
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UK government pressure
Asked about the announcement of compensation in the US by the Belfast Telegraph, Prime Minister David Cameron's spokeswoman said earlier this year: "It is for VW to explain the approach that they are taking in different jurisdictions. The Government has pressed VW on the issue of this kind of compensation.
"We expect VW to treat its UK customers fairly and to adequately address their concerns. The Transport Secretary has pressed VW on the specific issue of this discrepancy of compensation."
Despite growing pressure, VW has maintained that it does not believe it has broken any European emissions laws through the fitment of its test cheat software.
Compensation, buybacks offered to US customers
In the US, the offer to buy back cars at market value applies to all 500,000 2.0-litre diesel engined VWs caught up in the scandal. Presiding US district court Judge Charles Breyer gave scant details of the agreement during the US hearing but revealed that VW would also pay into an environmental fund and commit other money to promote green car technology.
Breyer only described the compensation offer as "substantial" but unconfirmed reports suggest VW will pay customers affected by dieselgate $5000 (about £3500) each. VW will also cover all the costs to remove defeat devices from affected cars, which were found to be running with software that enabled them to cheat emissions tests back in 2015.
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The car maker revealed it has set aside more than £12.6bn, with £6bn for repair or repurchase deals and the rest for litigation, including fines and legal fees.
VW lawyer Robert Giuffra described the first court agreement as a positive step in the firm's to win back customers: "Volkswagen is committed to winning back the trust of its customers, its dealers, its regulators and all of America. These agreements are an important step forward on the road to making things right."
Analysing the deal, Christian Stadler, Professor of Strategic Management at Warwick Business School, said: "What is still uncertain is whether this also resolves issues Volkswagen has with the US Justice Department. There is a pending civil suit and an on-going criminal investigation. If this deal manages to also resolve these issues it is really great for Volkswagen."
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Sam Sheehan and Jim Holder