Mueller spoke to workers today, one day after meeting with Environmental Protection Agency Administrator Gina McCarthy about the company's efforts to bring diesel cars into compliance with US law.
Volkswagen was forced to admit last year that about 600,000 vehicles were sold with illegal software designed to trick government emissions tests.
"We've made a mistake, and we have to fix this mistake," Mueller told The Associated Press after the speech on the floor of the Chattanooga factory. "Because it's so complicated, it takes a little time," Mueller said in the interview conducted in German.
"I understand the impatience that exists. I'm impatient, too. I'd also like a faster solution, but we have to proceed with care."
Mueller said the company has agreed with regulators not to discuss the next steps in public. In Detroit yesterday, EPA Director of Transportation and Air Quality Christopher Grundler said VW's proposed fixes fell short "in a lot of different areas," and the discussions are continuing.
Grundler wouldn't get into specifics, but said the agency and the California Air Resources Board are insisting on expeditious repairs that won't have an adverse effect on owners. "We're not there," he said.