For some time, storm clouds have been gathering over the less expensive end of the Swiss watch industry. Smartwatches, particularly the Apple Watch, have flooded the marketplace, inundating the production of traditionally styled Swiss watches that retail for less than $1,000.

But Tissot, the largest brand in that segment by estimated production volume and sales, says it is bucking the trend — although neither it nor its parent company, Swatch Group, disclose company performance.

“Globally, we are doing extremely well with double-digit growth,” said Sylvain Dolla, chief executive of Tissot, which primarily has watches at $250 to $2,000, a range in competition with Apple Watch. “The first eight months of this year were phenomenal.”

Such sales would be a significant improvement in the brand’s recent performance, according to the 2023 version of Morgan Stanley’s annual watch report, which estimates revenues for Switzerland’s top 50 watch brands by volume and sales.

The report estimated that Tissot’s turnover fell to 750 million Swiss francs in 2022 from 1.02 billion in 2019, a decline of 25 percent. If correct, Tissot has been pushed out of the Swiss watch industry’s top 10 by revenue and out of the so-called Billionaire Club, brands with annual revenues of more than 1 billion Swiss francs ($1.1 billion).

But Mr. Dolla, speaking on a video call from Tissot’s headquarters in Le Locle, Switzerland, where the company was established in 1853, said Morgan Stanley’s figures were wrong. “These statistics are from people who have no clue what we’re doing,” he said. “The reports don’t stress or motivate me.”

One of the authors of the Morgan Stanley report, however, said he believed Tissot’s 2022 revenues were even lower than the published estimate. Oliver Müller, who also is the founder of the Swiss consultancy LuxeConsult, wrote in an email, “Even if revenues are up by 10 percent this year, the brand would still be below the billion Swiss franc mark, which is still a negative trend compared to the market.”

This year has been a good one for watchmakers overall. The Federation of the Swiss Watch Industry, which tracks exports, reported in October that the export values of Swiss watches to the end of September had increased 8.6 percent year-over-year.

And Mr. Dolla’s claims of growth at Tissot had some support from data produced by Digital Luxury Group, a Geneva-based consultancy with offices in New York and Shanghai.

Using search volume as an indication of consumer interest, the group said the brand was searched for more than seven million times in July, a significant increase from the roughly two million searches it drew each month in mid-2020. Only Rolex, Omega and TAG Heuer performed better, according to the data, which did not include China, which Mr. Dolla said was “by far our No. 1 market.”

Why the surge in interest? Mr. Dolla said it was the result of repositioning the brand’s marketing to appeal to 20-somethings (For example, a 15-second YouTube video of Gen Zers wearing Tissot’s PRX35 model in a bowling alley setting that was posted Oct. 9 had drawn more than 2.5 million views nine days later). “We made a choice two years ago to put all our efforts in terms of content production into the young and ambitious,” he said. “They are the most inclined to buy watches.”

In 2021 Tissot introduced the PRX, a stainless steel sports watch that was based on a late 1970s model of the same name and was priced at $350 with a quartz movement and $675 with an automatic mechanical movement. Watches with links to the 1970s have stimulated sales and interest in recent years, led at the top end of the price universe by Patek Philippe’s Nautilus and Audemars Piguet’s Royal Oak.

Earlier this year, Tissot introduced iterations of the watch with dials in a robin’s egg blue that resembled Tiffany & Company’s famous signature color — echoing similar moves from Rolex and Patek Philippe in recent years. (At the peak of the market interest last year, the Rolex Oyster Perpetual 36 with a Tiffany dial was trading on the secondary market for more than three times its retail price.)

One U.S.-based retailer said he had seen rapidly growing demand for Tissot.

“It’s really resonated with the younger consumer, and demand has outstripped supply,” said Alan Zimmer, chief executive of the family-owned jeweler Reeds, which has about 60 stores in 13 states. He credited Tissot’s sponsorship of the National Basketball Association and the appeal of the PRX model, but said it was too early to tell whether the latest PRX release, a digital version with an L.C.D. screen, would also grow demand.

The success of the PRX is a contrast to Tissot’s efforts to compete with the wearable tech giants Apple, Garmin and Samsung. In 2020, Tissot introduced the T-Touch Connect Solar, a $1,095 solar-charged smartwatch version of its multifunction touch-screen T-Touch watch. The Solar had its own operating system, called SwALPS, and offered notifications, weather and altimeter functions, and trackers for activities such as hiking and cycling.

Sales, however, have been estimated as lackluster. “In 2022, Apple sold an estimated 40 million watches, while Tissot sold an estimated 30,000 T-Touch Connected watches,” Mr. Müller wrote in an email.

The T-Touch Connected Solar, “which doesn’t even allow you to connect to your Cloud data, not even WhatsApp, wasn’t introduced until 2020, by when the train had already left the station,” he noted.

Mr. Dolla said the T-Touch remained at the heart of his company’s strategy and that its sales and marketing were targeting health-conscious consumers aged 40 and older. As proof of the company’s commitment to the model, he described the 14,000-square-foot factory recently opened by the Swatch Group company Nivarox that is producing solar cells for Tissot’s digital and connected watches.

“T-Touch is niche,” he said. “I’m not interested in millions of units or consumer electronics where you have to recharge every day. We guarantee strong battery life and a watch that will be serviceable for years.”

Mr. Müller said T-Touch could only be niche. “It’s not selling anymore,” he wrote. “Twelve years ago, Tissot sold circa three million T-Touch watches. Now, it’s around 100,000, plus around 30,000 for the connected model. Who wants to buy this adventure watch, when Apple’s Watch has many more functions and full access to the Apple world?”

Mr. Dolla also cited Tissot’s investment in retail as proof of its growth. The company has 11,500 global points of sale, with 240 Tissot boutiques and 15 more being readied, he said.

One of those is an 8,800-square-foot boutique in London’s Covent Garden, and this month, Mr. Dolla said, the company expected to complete the 20 million euro ($21.1 million) acquisition of the 12,500-square-foot space it has been renting on the Champs-Élysées in Paris. “If the analysts’ figures were right,” he said, “we wouldn’t be making these investments.”

And, concerning declines among less expensive Swiss brands, he said, “For me, the only reason I can give for this fallout is that a lot of brands have abandoned this segment. The others went up in price. That’s why these figures are going down. We are alone now.”

While that change has helped grow Tissot, Mr. Dolla said, he added that he thought the shift posed a longer-term problem for the Swiss watch industry. “Collectively, we have to make sure the Swiss Made label has an answer to every segment of the market and to keep this dream of owning a Swiss watch.”