This is the second such statement from the firm. On Sunday, the carmaker released a statement from its global CEO saying he was "deeply sorry that we have broken the trust of our customers and the public", after the US Environmental Protection Agency (EPA) and the California Air Resources Board revealed manipulations to some of the firms cars that violated environmental standards.
Global CEO Martin Winterkorn's statement said the firm would cooperate fully with relevant agencies, adding: "We do not and will not tolerate violations of any kind of our internal rules or of the law."
Winterkorn also said public trust "is and continues to be our most important asset".
At an event in New York yesterday afternoon, VW America CEO Michael Horn reiterated this message of contrition, saying: "Let's be clear about this, our company was dishonest, with the EPA and the California Air Resources Board and with all of you.
"In my German words, we have totally screwed up."
He went on to say: "We must fix those cars to prevent this from ever happening again and we have to make things right with the government, our customers, our employees and also very importantly our dealers. This kind of behaviour I can tell you from the bottom of my heart is completely inconsistent with our core values."
It has subsequently been reported this morning that similar emissions violations were being investigated in Asia.
The firm's UK press office said it was not making any comment.
The scandal has already hit Volkswagen share prices, and could cost its reputation - last week PRWeek reported that the firm was one of the most trusted companies in the UK.