Sales for Stellantis STLA -5.73%▼ NV increased 32% in the second quarter, compared with the April-to-June period a year ago. The Jeep brand owner’s growth from the first quarter was more modest, up 3% in the second quarter compared with the first three months of the year.

Volkswagen AG VOW -3.54%▼ reported its best first-half U.S. sales in nearly a half-century while managing tight supplies. The company now has about 32,000 vehicles in inventory while aiming to sell around 30,000 vehicles a month, said Scott Keogh, chief executive of Volkswagen’s North American subsidiary.

“We’re losing some sales opportunities,” Mr. Keogh said.

The auto makers’ results mostly reflect analysts’ expectations that the rate of new-car sales growth is beginning to fall off from recent months, when car shoppers turned out in near-record numbers, buoyed by excess household savings and pent-up demand from the pandemic.

Customers are still clamoring for a new ride, dealers say. But it has become harder for salespeople to match buyers to vehicles because of the lack of inventory resulting from a computer-chip shortage that has hobbled car production since winter.

“We really don’t have enough cars to go around,” said Joe Shaker, owner of Shaker Automotive Group, which sells several brands in Connecticut and Massachusetts. He said his Ford F -1.81%▼ store is carrying about 14% of its normal inventory.

New-vehicle sales in the first half of the year are expected to reach about 8.3 million units, according to an estimate from J.D. Power, a 32% increase over the same period in 2020 and up nearly 1% from the first half of 2019.

The rate of sales slowed considerably at the end of the second quarter, falling to an annualized selling pace of 15.4 million, according to research firm Wards Intelligence. That is down from April, when the industry was on pace to sell nearly 19 million vehicles for the year. The industry tracks the annualized sales rate as a measure of market strength from month to month because it strips out seasonal factors.

Analysts attribute the deceleration to withering dealership inventory. Dealers started June with about 1.5 million vehicles on their lots or en route to stores, down 42% from the same time in 2020 and down 23% from the start of May, according to Wards Intelligence. The diminishing selection is driving prices to record highs.

The average new vehicle sold eclipsed $40,000 for the first time in June, according to an estimate from J.D. Power, with car shoppers routinely paying above sticker price.

“We’ve been in a full-fledged supply crisis since about June of last year,” said Tyson Jominy, automotive analyst for J.D. Power. “Meanwhile, we have very, very robust demand among some of the wealthiest consumers.”

Consumers are flush with savings from federal stimulus payments and from hunkering down during the pandemic. Interest rates remain at historically low levels and used-car values have soared, giving consumers higher trade-in values when buying a new vehicle.

The unusual market dynamics—bare dealership lots, eager shoppers and heady pricing—are expected to last at least through the end of the year, analysts and car executives say. Despite the dynamics, many auto makers and dealership groups have reported record profits in recent months, bolstered by the stronger pricing and lower costs.

Bob Carter, Toyota Motor Corp.’s North American sales chief, said strong consumer confidence helped the company to its strongest first five months of the year ever, despite having to manage a raft of supply-chain problems.

“We have lots of problems, but I have zero complaints,” he said.

Toyota TM -1.00%▼ typically would have roughly 330,000 Toyota and Lexus models on dealer lots in June. It expected dealers to finish the month with around 70,000 vehicles on hand, Mr. Carter said.

Toyota’s second-quarter sales increased 73% over the prior year, but showed signs of slowing in June, down about 35,000 vehicles from the month before. Rival Honda Motor Co. HMC -2.68%▼ reported a second-quarter sales increase of nearly 66%, while its rate of sales also declined in June from May.

Hyundai Motor Co. reported its best-ever second quarter, selling 240,005 vehicles in the April-to-June period. That is a 69% increase from the quarter a year ago. The pace slowed in June, when the company sold 72,465 vehicles, down significantly from May when they sold more than 90,000 cars.

Kurt McNeil, GM’s vice president of U.S. sales operations, said GM dealers have less than a week’s worth of supply of large sport-utility vehicles, whereas normally they would have enough inventory to last three months.

He said GM expects the semiconductor shortage to ease, but he doesn’t see the situation on dealer lots improving much before the end of the year, and expects inventory to be constrained through 2022. GM said Thursday it ended the second quarter with 211,974 available vehicles, compared with 334,628 at the end of the first quarter.

“There’s so much demand that vehicles are just going to sell” as soon as they hit dealer lots, Mr. McNeil said. “We’re just going to be drastically low for the foreseeable future.”

Pickup trucks and SUVs, significant profit generators for GM and rivals Ford Motor Co. and Stellantis, have been disproportionately hurt by the chip shortage, according to data from research firm LMC Automotive. As a result, the Detroit companies posted falling market shares through the first five months of the year, while Toyota, Honda and Hyundai gained, LMC said.

Toyota outsold GM by about 46,500 vehicles in the second quarter, the first time in more than 20 years that any company has outsold GM, and the first quarter ever that the Japanese auto makers has outsold its Detroit rival, according to car-shopping website Edmunds.com.

On Wednesday, Ford said the chip shortage will force it to cut output across more than a half-dozen U.S. factories in July.

Auto makers in general have given priority to the production of their most popular models, while dealers have begun to assign incoming vehicles to customers in an attempt to expedite shipments to their stores.

Subaru Corp. FUJHY -0.15%▼ said it has sold 20% more vehicles in 2021 relative to last year. The Japanese auto maker blamed the chip shortage for the rally stalling in June, however, when it sold 20% fewer cars than in the same month last year.

Higher used-vehicle prices also are helping drive new-car sales, analysts say, because shoppers are eager to leverage the higher value of their trade-ins. Used-vehicle prices on average were up an estimated 36% in mid-June from a year earlier, according to auction firm Manheim Inc.

The hot used-car market and dearth of shipments from the factory have left car dealers scrounging to feed their pre-owned vehicle lots.

Mr. Shaker said the new-vehicle selling price is no longer his priority in negotiations. Instead, he is telling salespeople to find customers who have a used vehicle they are willing to trade in.

“Right now, it’s far more important for us to sell to someone with a trade-in, because we need more vehicles to sell,” Mr. Shaker said. “When you’re running out of cars, a customer with a trade at least gives you two bites at the apple.”

– Ben Foldy contributed to this article.