Volkswagen announced plans yesterday to refit up to 11 million vehicles and overhaul its namesake brand following the scandal over its rigging of emissions tests.

New chief executive Matthias Mueller said the German carmaker would ask customers “in the next few days” to have diesel vehicles that contained illegal software refitted, a move which some analysts have said could cost more than €5.8 billion.

Europe’s biggest carmaker has admitted cheating in diesel emissions tests in the United States. Germany's transport minister says it also manipulated them in Europe, where Volkswagen sells about 40 per cent of its vehicles.

The company is under huge pressure to address the worst business crisis in its 78-year history, which has wiped more than a third off its market value, sent shock waves through the global car market and could harm Germany's economy. “We are facing a long trudge and a lot of hard work,” Mueller told a closed-door gathering of about 1,000 top managers at Volkswagen's Wolfsburg headquarters on Monday.

We will only make progress in steps

"We will only be able to make progress in steps and there will be setbacks," he said, according to a text seen by Reuters.

Volkswagen did not say how the planned refit would make cars with the “cheat” software comply with regulations, or how this might affect vehicles' mileage or efficiency, which are important considerations for customers.

Manipulating emissions results allowed Volkswagen to keep down engine costs in a "clean diesel" strategy that was popular in Europe and at the heart of a drive to improve US results.

Mueller was appointed CEO last Friday to replace Martin Winterkorn. German prosecutors said on Monday they were investigating Winterkorn over allegations of fraud.The crisis is an embarrassment for Germany, which has for years held up Volkswagen as a model of its engineering prowess.