In a statement published by the carmaker on Sunday, Chief Executive Officer Martin Winterkorn said, "I personally am deeply sorry that we have broken the trust of our customers.
"Volkswagen has ordered an external investigation of this matter," he said.
The US Environmental Protection Agency (EPA) said on Friday the software deceived regulators measuring toxic emissions, adding that Volkswagen could face fines of up to $18 billion as a result.
The Detroit News reported late Friday that VW dealers still had some 2015 diesel Jetta, Passat and Beetle cars for sale.
A VW representative on Sunday confirmed the partial halt of sales of the affected vehicles but did not give any numbers.
Winterkorn said, "We do not and will not tolerate violations of any kind of our internal rules or of the law," adding that the company was fully cooperating with the relevant agencies.
He gave no details on who would carry out the external investigation.
"This is not your usual recall issue, an error in calibration or even a serious safety flaw," Bernstein analysts wrote in a note on Sunday.
"There is no way to put an optimistic spin on this - this is really serious." Cynthia Giles, an enforcement officer at the EPA, said on Friday the cars in question "contained software that turns off emissions controls when driving normally and turns them on when the car is undergoing an emissions test".
The feature, which the EPA called a "defeat device," masks the true emissions only during testing. When the cars are on the road, they emit as much as 40 times the level of pollutants allowed under clean air rules meant to ensure public health is protected, Giles said.
"We have admitted to it to the regulator. It is true. We are actively cooperating with the regulator," a Volkswagen spokesman said on Sunday.
Volkswagen could face civil penalties of $37,500 for each vehicle not in compliance with federal clean air rules. Some 482,000 four-cylinder VW and Audi diesel cars sold since 2008 are involved in the allegations.
If each car involved is found to be in noncompliance, the penalty could be $18 billion, an EPA official confirmed during the telephone conference on Friday.
Volkswagen peer Daimler, meanwhile, signalled it may not be subject to the same violation.
"I have a rough idea of what is happening and that it does not apply to us," Daimler Chief Executive Dieter Zetsche said on Sunday at an event in Hamburg.
"But it is much too early to make a final statement on this," he added.
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