Volkswagen chief executive Martin Winterkorn has resigned following the revelation that the firm manipulated US diesel car emissions tests.
Mr Winterkorn said he was "shocked" by recent events and that the firm needed a "fresh start".
He added that he was "not aware of any wrongdoing on my part" but was acting in the interest of the company.
VW has already said that it is setting aside €6.5bn (£4.7bn) to cover the costs of the scandal.
The world's biggest carmaker admitted last week that it deceived US regulators in exhaust emissions tests by installing a device to give more positive results.
The company said later that it affected 11 million vehicles worldwide.
"I am clearing the way for a fresh start with my resignation," Mr Winterkorn said in his statement.
He said he was "stunned" at the scale of the misconduct in the group but that he was confident that VW would overcome this "grave crisis".
"The process of clarification and transparency must continue. This is the only way to win back trust," he continued.
In a separate statement, the supervisory board said they would announce Mr Winterkorn's successor at a board meeting on Friday, adding that it was "expecting further personnel consequences in the next days" as a result of its own investigations.
"The internal group investigations are continuing at a high tempo," it said.
"All participants in these proceedings that has resulted in unmeasurable harm for Volkswagen will be subject to the full consequences."
There has been speculation in German newspapers that Matthias Mueller would be named as the next chief executive. He is head of Porsche, which is part of the Volkswagen group of companies.
The board also said that it would voluntarily submit a complaint to the state prosecutors.
"In the view of the Executive Committee criminal proceedings may be relevant due to the irregularities," its statement said.
German public prosecutors have already said they are considering an investigation, with US authorities also said to be planning criminal investigations.
Speaking to Radio 5 live Martin Leach, chairman of car industry consultancy Magma Group and former president and chief operating officer of Ford Europe, said the scandal was "not the work of a rogue engineer... so there would have been a number of people who knew of this device".
Mr Leach added: "Nobody knows just how bad this could get for Volkswagen."
'A real shock'
Volkswagen shares have tumbled some 30% since the beginning of the week in response to the scandal, which has stunned investors.
"It has been a real shock. We are a long-term shareholder and we put a lot of emphasis on management credibility," said Gilles Guibout, a fund manager at AXA Investment Managers, which is the ninth biggest shareholder in VW.
He said that the departure of Mr Winterkorn "is an attempt to keep the fire under control", but added that it is not clear if "this will be enough".
While VW has set aside €6.5bn to cover potential costs of the scandal, Mr Guibout thinks the bill is more likely to be €10bn.
In addition, VW faces fines of up to $18bn by the regulator, the Environmental Protection Agency (EPA).
Trouble for diesel?
In the UK half of cars sold have diesel engines and many drivers will be wondering if they can trust performance figures quoted when they bought their car.
Volkswagen is the only company to have admitted to cheating over emissions testing.
Its Jetta, Beetle, Golf and Audi A3 models in the US from 2009 to 2015, and the Passat from 2014-15, had the devices which produced doctored results.
The director of the RAC Foundation Steven Gooding, says the affair has been damaging, though he does not agree with predictions that diesels will now be labelled as dirty and are on the way out.
"It's a bit too early to be saying that this is the beginning of the end for the diesel engine.
"I think the key thing is we all need to be confident that the new diesels coming through - they're called the Euro6 Test diesels - are really performing as we need them to and as we expect them to," he said.