New Volkswagen Chief Executive Matthias Mueller said the German manufacturer will ask customers with some diesel models to come in "in the next few days" for modifications.

Those that contained illegal software will have to be refitted, the company announced - a move which some analysts have said could cost more than $6.5 billion.

It comes after Volkswagen was forced to apologise last week when it was discovered it had developed the software in order to trick emission tests in the US for some of its diesel models.

Mr Mueller told a closed gathering of top managers at the company's Wolfsburg headquarters: "We are facing a long trudge and a lot of hard work.

"We will only be able to make progress in steps and there will be setbacks."

On Monday, Audi said 2.1m of its cars were fitted with the same emission cheating software.

On the same day, Volkswagen was said to have suspended the research and development heads of Audi, Volkswagen's core passenger car division and sports car maker Porsche.

VW is the parent owner of Audi and Porsche.

The vehicles affected are those with the so-called EU5 engines. Newer cars with EU6 engines are said to be unaffected.