Over all, auto sales in May fell 0.9 percent, to 1.5 million cars and light trucks. It was the fifth consecutive monthly decline and further underscored that the auto industry is slowing down after seven straight years of growth.
Michael J. O’Brien, Hyundai’s vice president of corporate and product planning in the United States, acknowledged that the company’s car-heavy model line was out of step with consumer tastes.
“We have work to do,” he said. “We are very well aware of where the market is.”
Hyundai attributed last month’s sales decline to a reduction in sales of cars to fleet customers like rental car companies. But sales of its Santa Fe S.U.V. also slumped.
And in a clear sign of a soft sales market, the company is offering heavy discounts. This week, for example, Grappone Hyundai in Bow, N.H., was advertising a fully loaded 2017 Sonata for $26,346 — more than $9,200 below its list price. Other models had discounts of $4,000 to $6,000, price cuts that would have been unimaginable five years ago.
“This seems to be resonating with the public,” said Larry Haynes, president of the Grappone Automotive Group. “It’s definitely helping us.”
Some of the discounts are aimed at helping dealers with an unusual problem: A number of 2016 models remain unsold in dealer inventories. Mr. DiFeo’s franchise still has six.
The price-cutting is taking a toll, though. The company blamed sales incentives in the United States for a sharp drop in earnings in the fourth quarter of 2016, and cited them as a factor when it reported another decline in the first quarter of this year.
The American consumer’s swing toward bigger vehicles is one of the biggest changes automakers have seen in decades. Just four years ago, vehicles classified as light trucks, which include S.U.V.s and most crossovers, made up half of the American market. In the first five months of this year, 62 percent of all new vehicles sold were from the category.
The trend is roiling big parts of the industry. Fiat Chrysler Automobiles stopped making small and midsize cars last year and is converting two idled car plants to make Jeeps and trucks. A year ago, Ford Motor announced it would build a new small-car plant in Mexico, then canceled the plan in January. The company came under heavy criticism from President Trump for investing in Mexico, but finally said it no longer needed the additional production capacity because of falling demand for small cars.
Hyundai, based in South Korea, has taken hits in two ways. The company’s affiliate, Kia, also relies on small and midsize cars for most of its sales. So far this year, Kia’s sales in the United States have fallen 9.8 percent. Hyundai owns a large stake in Kia. They develop new models jointly and share a factory in West Point, Ga.
Hyundai’s troubles may also linger for some time.
Other automakers caught flat-footed by the shift have spent the last few years adding more S.U.V.s, especially the lighter crossovers. Volkswagen, for example, has long relied on sales of its Jetta and Passat sedans. But it added a redesigned Tiguan S.U.V. last year, is rolling out a hulking model called the Atlas this year and has a compact crossover coming next year.
In contrast, Hyundai has invested in the wrong direction. The new models it is now rolling out include two luxury sedans sold under the Genesis brand name; the Ioniq, a hybrid compact; and a redesign of the midsize Sonata, due next year.
All are in segments whose sales are declining. In the first three months of the year, luxury car sales fell 12 percent, according to the researcher Autodata. Sales of midsize sedans like the Sonata fell 17 percent.
The new cars will sell well, Mr. O’Brien said. “At the end of the day, there’s still plenty of volume in the sedan area,” he said. He added that the company was working to increase production of its existing S.U.V.s — the Tucson, Santa Fe and Santa Fe Sport.
It typically costs about a billion dollars to develop a car from the ground up. The Ioniq was designed to compete with the top-selling hybrid, the Toyota Prius. The Ioniq is rated to go 55 miles on a gallon of gasoline — three more than the Prius.
Even so, the Hyundai car faces considerable headwinds because fewer Americans are interested in hybrids. Prius sales are down 17.8 percent this year.
“Did somebody guess wrong?” Mr. DiFeo said. “Perhaps.”
Nevertheless, he said he felt Hyundai was poised for a resurgence. A new small S.U.V., the Kona, should arrive next year, followed by a redesign of the Santa Fe Sport then and a new large S.U.V.
“I think those vehicles will really make an impact,” he said. “Right now, we just have to stay focused until we get to that point.”