DETROIT — Ever since Volkswagen admitted in September to cheating on diesel emissions tests in the United States, its sales and grand plans for growth in the American market have taken a nosedive.

Now, executives of the German automaker are embarking on what is perhaps the ultimate hard sell — trying to win back consumers at the annual Detroit auto show and, later this week, persuading regulators that VW has found a way to fix the problem.

The campaign started on Sunday with the first public appearance in the United States by its chief executive, Matthias Müller, since the emissions scandal snowballed into the biggest crisis in Volkswagen’s history.

Mr. Müller faces multiple challenges — broken trust with car owners, frayed relations with dealers and increasingly fractious dealings with regulators.

On Wednesday, he will meet with federal regulators in Washington about when Volkswagen will fix nearly 600,000 cars in the United States — among 11 million affected worldwide — equipped with devices that evaded emissions standards.

Already, Volkswagen executives have been laying the groundwork. On Sunday ahead of the North American International Auto Show in Detroit, Mr. Müller said: “We know we deeply disappointed our customers, the responsible government bodies, and the general public here in the U.S. I apologize for what went wrong at Volkswagen. We are totally committed to making things right.”

He also made a promise that reflects the scale of the damage done to Volkswagen’s reputation in the marketplace.

“We are now creating a different and better company, a new Volkswagen,” he said.

That is hardly the brash attitude that executives took on previous visits to the Detroit show, when the former chief executive, Martin Winterkorn, vowed to ratchet up Volkswagen brand sales in the American market to 800,000 vehicles 2018.

But in the wake of the emissions debacle, Mr. Winterkorn has resigned, the company is under criminal investigation in the United States, Europe and elsewhere, and the Volkswagen brand has been hammered in the American market.

While industry sales rose 6 percent in 2015 to set an annual record of 17.5 million vehicles, Volkswagen brand sales sank 5 percent, to 349,000 vehicles — just slightly over 2 percent of the overall market.

The company was already having trouble competing in the United States with market leaders like General Motors, Ford Motor and Toyota before its emissions problems.

But then it had to indefinitely freeze sales of its diesel cars, which are among its most popular models with American buyers. And as its reputation continues to plummet along with its sales, Volkswagen is under intense pressure to somehow restore its image.

Few in the industry think Volkswagen, despite the huge financial liabilities it faces from the emissions crisis, would ever leave the United States market, where it has invested billions of dollars building a dealer network and is expanding an assembly plant in Tennessee.

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“For them to back away from the U.S. market is not realistic,” said Karl Brauer, an analyst with the research firm Kelley Blue Book. “They just cannot cede this market to their competitors.”

Two company executives based in the United States, who spoke on condition of anonymity because they are not authorized to comment on the emissions issue, said there have never been internal discussions about pulling out of the American market.

And Mr. Müller said Sunday, “The U.S.A. is and remains a core market for the Volkswagen Group.”

Volkswagen is grappling with the emissions mess by raising incentives on its vehicles to stir more demand, and giving dealers financial credits for diesel cars on the lot that they cannot sell.

One Volkswagen dealer called the credits a “stopgap” measure to help offset losses by dealers stuck with tainted diesel cars and a slowdown in consumer traffic.

“No doubt our stores have been affected,” said Jason Kuhn, who sells about 2,000 Volkswagen brand vehicles a year at his three dealerships in Florida and Georgia. “We employ about 150 people, and they are anxious about making sure there will be a paycheck for them.”

The wave of publicity about how Volkswagen cheated on emissions tests has raised suspicions among Americans who previously had a high opinion of the brand.

“I wouldn’t buy any VW until I see their resolution,” Aleese Heinzman, a Michigan resident, said as she visited a General Motors exhibit on Saturday near the auto show. “Even then, you never know what’s going to happen in the next few years, or what else they are hiding.”

Another Michigan woman at the exhibit, Becky Lasecki, said she hoped to buy a new fuel-efficient car this year, but had crossed Volkswagen diesel models off her list.

• “Volkswagen always made good cars,” she said. But, she added, “I know they were less than honest.”

One way the company is coping is by pouring on sales incentives to stimulate demand. Kelley Blue Book estimated that Volkswagen offered $4,500 worth of incentives on its cars and sport utility vehicles in December, among the highest of any automaker and nearly double the $2,500 it spent in the same month a year earlier.

Dealers are scrambling to play down the impact of the legal troubles surrounding Volkswagen’s sales of diesel-powered cars that spewed 40 times the amount of pollutants allowed by federal rules.

“A lot of manufacturers have gone through major incidents when it comes to recalls,” said Nick Ort, general manager of a Volkswagen dealership in Perrysburg, Ohio. “Yes, VW cheated the system, but the vehicles didn’t break down, and there was no loss of life.”

Another dealer said that current owners of Volkswagen diesel cars were confused about the repairs the company was planning for affected models, and how the repairs would affect performance on the road.

“People feel like the fix will ruin the car,” said Jonathan Drouillard, who manages a used-car lot in Royal Oak, Mich., that sells older-model Volkswagens.

Mr. Kuhn said dealers were desperate for more information from Volkswagen’s German executives, who have also been accused by various attorneys general in the United States of being uncooperative in investigations.

“History has proven that the quicker the corporation gets a resolution, the better it is for consumers and dealers,” he said. “My hope is that they stay keenly aware of this.”

On Monday, Volkswagen was expected to unveil a new concept version of its Tiguan S.U.V. at the Detroit show. The company is already lagging badly in the market for S.U.V.s, which has been a prime driver of the industry’s overall record sales levels.

In any other year, a new S.U.V. would be seen as a big step toward reaching Volkswagen’s ambitious sales goals. But with Mr. Müller on his way to a showdown with regulators, including the head of the Environmental Protection Agency, it is unlikely the finer points of the new Tiguan will get much attention.