Continuing disruptions from the Covid-19 pandemic and a worsening global semiconductor shortage hammered the automotive industry in the third quarter as the world’s largest car makers reported steep falls in earnings and production and dealers struggled to source models.

In Europe, the two largest manufacturers, Volkswagen AG and Stellantis NV, said Thursday that production of new vehicles plunged 35% and 30% respectively in the three months to Sept. 30, as the dearth in semiconductor components caused unfinished cars to pile...

Continuing disruptions from the Covid-19 pandemic and a worsening global semiconductor shortage hammered the automotive industry in the third quarter as the world’s largest car makers reported steep falls in earnings and production and dealers struggled to source models.

In Europe, the two largest manufacturers, Volkswagen AG and Stellantis NV, said Thursday that production of new vehicles plunged 35% and 30% respectively in the three months to Sept. 30, as the dearth in semiconductor components caused unfinished cars to pile up in factories.

The supply of chips needed for core components for vehicles slowed to a trickle in the third quarter, affected by disruptions of chip production in Asia and the U.S. from the impacts of the pandemic, fierce storms in Texas, and the fallout from a fire at a supplier in Japan earlier this year.

“This all slowed down the strong recovery we had in the first half of the year,” VW Chief Executive Herbert Diess told reporters Thursday.

In the U.S., General Motors Co. and Ford Motor Co. said late Wednesday that third-quarter profit and output fell sharply as a result of the chip crunch, saying the lack of chips would continue to dent production and leave dealership lots nearly empty well into next year.

The number of semiconductors in a modern car, from the ignition to the braking system, can exceed a thousand. As the global chip shortage drags on, car makers from General Motors to Tesla find themselves forced to adjust production and rethink the entire supply chain. Illustration/Video: Sharon Shi The Wall Street Journal Interactive Edition

In broadly weaker global stock markets, automotive shares came under pressure as quarterly earnings rolled in. VW’s widely traded preference shares fell sharply in opening trading and were down 3.29% by late morning. Stellantis shares initially rose in early Milan trading, but fell back by midday when they were trading nearly unchanged from the previous close. Shares of Bayerische Motoren Werke AG , which reports next week, were down 1.5%, while Daimler AG , which reports Friday, were trading 0.7% lower.

European auto shares followed the downward trend in the U.S. and Asia. GM shares closed 2.1% lower on Wednesday, and Ford closed down 2.7%. Toyota Motor Corp shares were down 0.2% and shares of Nissan Motor Co. , Japan’s second-largest auto maker, were down 0.85%.

Looking ahead, auto executives expressed some optimism that chip supplies have begun to stabilize but stressed that the shortages and their impact on production would continue to be felt in 2022.

“The visibility on semiconductors continues to be a difficult subject for the industry and for us. I think now we’re on a better track and we’re seeing some stabilization of supply and improvement in our month over month production,” Stellantis Chief Financial Officer Richard Palmer told reporters on Thursday.

Mr. Diess said the chip shortage likely peaked in the third quarter, but constraints would continue at a reduced level because it will take the semiconductor manufacturing industry time to expand capacity.

“We should be through the worst now,” he said. “The situation will ease but this will be a continuing struggle for us.”

The impact of the shortages on earnings was mixed.

VW operating profit before special items fell 12% to 2.8 billion euros, equivalent to $3.25 billion, with a corresponding margin of 4.9% for the period, the company said in its interim report. Revenue fell 4.1% to €56.93 billion but beat analysts’ expectations of €54.66 billion compiled by FactSet. After-tax profit was up 5.6% to €2.90 billion.

For 2021, Volkswagen reiterated its forecast to achieve an operating return on sales between 6.0% and 7.5%. However, it lowered its full-year guidance for deliveries to customers, which are now expected to be unchanged from last year.

VW said revenue is expected to be considerably higher than in 2020, but VW Chief Financial Officer Arno Antlitz stressed that the chip shortage showed the company needed to press harder to improve productivity.

“After a record result in the first half of the year, the semiconductor shortage in the third quarter made it clear that we are not yet sufficiently resilient to fluctuations in factory utilization,” he told reporters.

Stellantis, which typically doesn’t report profit in the first and third quarters, said sales fell 14% world-wide to €32.6 billion. The company confirmed its profitability goal for the year.

The lack of new vehicles on dealer lots has led to a boom in used-car sales, which was a big profit driver for VW in the third quarter through higher financing revenues at VW’s in-house bank, Mr. Diess said.

To adapt to the shortage, VW also reallocated chips to higher-margin vehicles and raised prices.

GM, which cut vehicle shipments in North America by nearly half in the July-to-September period, said Wednesday that its net profit dropped 40% in the third quarter, while Ford reported a 23% decline in net income compared with the same year-ago quarter.

GM finance chief Paul Jacobson said the impact of the chip shortage should lessen gradually over 2022 but didn’t see a strong recovery of production.

“In terms of what we’re seeing in demand, I think the opportunities to build inventory are going to be somewhat limited,” Mr. Jacobson said, adding that short supplies are expected to keep consumer prices elevated.

Ford finance chief John Lawler said the chip shortage should ease next year and Ford expects to boost deliveries to dealerships by about 10%.

—Kim Richters in Barcelona and Mike Colias in Detroit contributed to this article.

Write to William Boston at william.boston@wsj.com and Nick Kostov at Nick.Kostov@wsj.com