About 482,000 of those cars equipped with the cheating system were sold in the United States, according to the Environmental Protection Agency. Those will have to be recalled and fixed. Car dealers are also stuck with hundreds of diesel-engine cars on their lots that they can no longer sell until Volkswagen fixes the emission problem.

“We are sitting here doing the best we can, and we’re waiting patiently along with the rest of our customers to see what Volkswagen decides to do,” said Lance Willis, the general manager of a Volkswagen dealership in the Woodlands, Tex.

Three days after admitting to its deception, Volkswagen told its dealers that it would provide financial guarantees and extra bonuses to “stabilize your profitability in the near term.”

It also stressed in another dealer communication that the problem did not affect the safety of its vehicles and that the company was working hard to find a solution, a message it has since posted on its public social platforms.

“We understand the pressure these recent events have put your business under, and we are committed to providing you support,” the letter said, which was signed by Michael Horn, the chief executive of the Volkswagen Group of America.

As part of its financial support, Volkswagen said it would offer to reimburse dealers for the cost of holding on to diesel cars affected by the sale freeze until repair instructions were released. The company will also pay dealers $300 for any new gasoline-powered car they sell, $600 for Passat models and will guarantee extra bonus compensations for dealers for cars sold in the third and fourth quarter this year.

Relations between Volkswagen and its dealers have been increasingly tense in recent years. Until Mr. Horn was appointed in 2014, dealers complained that their voices were not being heard by the company’s leadership in Germany. They warned that the overly ambitious goal of selling 800,000 cars by 2018 would not be met and said the company’s lineup needed cars that were better adapted to the American market.