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 $6.5 billion.
Europe's biggest carmaker has admitted cheating in diesel emissions tests in the United States and Germany's transport minister says it also manipulated them in Europe, where Volkswagen sells about 40 percent 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 late on Monday.
"We will only be able to make progress in steps and there will be setbacks," he said, according to a text seen by Reuters.
Mueller was appointed CEO on 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 and has lobbied against some tighter regulations on automakers. The German car industry employs more than 750,000 people and is a major source of export income.
Germany's KBA watchdog had set Volkswagen an Oct. 7 deadline for it to present a plan to bring diesel emissions into line with the law.
Millions of cars
Volkswagen said previously about 11 million vehicles were fitted with software capable of cheating emissions tests, including 5 million at its VW brand, 2.1 million at luxury brand Audi, 1.2 million at Czech division Skoda and 1.8 million light commercial vehicles.
Refitting 11 million cars would be among the biggest recalls in history by a single automaker, similar in scale to Toyota's recall of more than 10 million vehicles between 2009 and 2010 over acceleration problems, though dwarfed by the number recalled by multiple carmakers due to faulty Takata airbags.
Volkswagen sold 10.1 million vehicles in the whole of 2014.
The company said last week it would set aside 6.5 billion euros ($7.3 billion) in its third-quarter accounts to help cover the cost of the crisis.
But analysts think that may not be enough, as it faces potential fines from regulators and prosecutors, as well as lawsuits from cheated customers.
Sweden's chief prosecutor told Reuters on Tuesday he was considering whether to start a preliminary investigation into Volkswagen.
At 1045 GMT, Volkswagen shares were down 0.2 percent at 99.1 euros.
Mueller also said Volkswagen's core VW division, struggling with high-fixed costs and low profit margins, would be given more autonomy, akin to the independence enjoyed by premium flagship brands Audi and Porsche.
Analysts have long urged the company to tackle the underperformance of its core mass-market brand, and in particular to dilute control from the centre which has been blamed for product delays and problems adapting to local markets.
Klaus Mohrs, the mayor of Wolfsburg where Volkswagen employs around 70,000 people, said on Monday he expected a sharp decline in business taxes as a result of the crisis, and announced an immediate budget freeze as well as a hiring ban.
The emissions scandal has sent ripples through the global car market, with manufacturers fearing more costly regulations and a drop in diesel car sales.
The European Commission is working on outline plans to reform the European system for approving new models of cars by the end of the year.
Volkswagen's Belgian importer, D'Ieteren, said it would offer engine upgrades to 800 customers who had ordered a vehicle with a diesel engine that was likely to have been fitted with illegal software. The importer said it would pay for the expected 2 million euros cost.
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