Volkswagen has admitted 11 million of its cars worldwide are fitted with software which masks the true emissions of vehicles while they are being tested.
The scandal has wiped out more than a third of the company's value on stock markets in two days.
Volkswagen chief executive Martin Winterkorn said he was endlessly sorry and promised to clear up the crisis.
"We do not and will not tolerate violations of any kind of our internal rules or of the law," Mr Winterkorn said.
Volkswagen US group chief executive Michael Horn said the company "totally screwed up", had been "dishonest" and that their actions went against their own "values".
Last Friday, US regulators said VW diesel cars had much higher emissions than tests had suggested. Some other governments have announced they will also investigate.
Volkswagen New Zealand said the cars it has sold here were sourced from Europe, where emissions testing standards were different to those in America, where the software was used.
Lawyers file action, US investigates
Lawyers have filed at least 25 class actions on behalf of scores of car owners across the United States.
The car-owners involved in the lawsuits said they were hooked into buying Volkswagen vehicles wih ads claiming the cars were clean, smart and eco-friendly.
Class action lawyers have been able to act quickly as many of their friends and colleagues own the cars.
The US Justice Department has started a criminal investigation into several VW and Audi diesel models.
French Finance Minister Michel Sapin has called for a European Union inquiry but a British car industry spokesman said there was "no evidence" of cheating.
British Society of Motor Manufacturers and Traders chief executive Mike Hawes said the EU operated a "fundamentally different system" from the US, with tests performed in strict conditions and witnessed by a government-appointed independent approval agency.
"There is no evidence that manufacturers cheat the cycle," he said.
"Vehicles are removed from the production line randomly and must be standard production models, certified by the relevant authority - the UK body being the Vehicle Certification Agency, which is responsible to the Department for Transport."
However, he also described current testing methods as "outdated" and said the car industry wanted an updated emissions test, "more representative of on-road conditions".
In addition to paying for the recall, VW faces fines that could add up to billions of dollars. There may also be criminal charges for VW executives.