Next Issue Media, the mobile app often described as the Netflix of magazines, is trying to introduce itself to a wider audience this holiday season with a marketing campaign that includes TV commercials on 21 cable networks, the company said. The effort comes, however, just as Next Issue Media is getting a new competitor with a similar product.

The goal of the campaign, which also includes print and Google search ads, is to get Next Issue Media's all-you-can-read service to somewhere between 75,000 and 100,000 subscribers, including newcomers on the 30-day free trial period, according to Morgan Guenther, Next Issue Media's CEO.

Mr. Guenther declined to say how many subscribers the service has now, but said the campaign target isn't a big reach. "We'll be disappointed if we're not in that range," he said.

About 75,000 subscribers to individual magazines also use the app to read digital editions of those magazines, a service Next Issue Media offers publishers that doesn't bring it any revenue but exposes more people to its platform, Mr. Guenther said.

Next Issue Media expects subscription revenue this year of $12 million to $15 million, which it will share with participating publishers. A spokesman for the company declined to describe the revenue split. Next Issue Media does not take a cut of any advertising revenue from magazines on the app.

When Next Issue Media debuted first on Android devices and then the iPad in 2012, it offered a product familiar to many Netflix viewers but essentially unknown in the magazine world: for $9.99 a month, subscribers could access digital editions of about 40 monthly and bimonthly magazines; for $14.99 a month, the app included weeklies too. Its menu included top titles from Conde Nast, Hearst, Meredith and Time Inc., all of which are investors in the company. (News Corp. is also an investor.) The app, which subsequently added an iPhone version, now has 122 titles, with plans to add another 8 to 10 magazines by the end of this year. It added some Canadian titles last month after Rogers Media bought an equity stake in the company.

But consumers still don't know enough about the service, according to Mr. Guenther. "We're one of 900,000 apps in the Apple app store," said Mr. Guenther, former president of TiVo. "No one really knows about us. What we're really trying to do with the campaign is get some reach and frequency through the seasonal opportunity and the first quarter of next year."

Two 30-second spots, one geared towards women and the other aimed at men, started running this week on Fox News, CNN, MSNBC, Lifetime, Bravo, Food Network and AMC, among others. Angry Little Dog out of San Francisco created the spots, a spokesman for Next Issue Media said. The print pieces were done by New York-based agency O2, according to the spokesman.

Next Issue Media's struggle to gain widespread traction among tablet users is not unlike that of the publishers investing in the company. Digital editions, once seen by some as a new growth engine for the magazine industry, comprised just 3.3% of circulation in the first half of 2013, according to the Alliance for Audited Media.

There's also a bit of a standing question about Next Issue Media's business model, namely whether it might chip away at publishers' revenues. Why pay $20 for two or three magazine subscriptions when Next Issue Media offers so many more titles for half the cost?

"Our formula is more people spending more time reading more magazines," said Mr. Guenther, adding that there's little crossover between print subscribers and Next Issue Media's digital subscribers. "If you can make that happen the boats rise for the entire industry."

The company also plans to further its emulation of Netflix in the second and third quarter quarter of next year, when it plans to start letting users search its trove of magazines for specific topics and to introduce a recommendation engine based on a subscriber's interests.

"It's a natural evolution of an on-demand, all-you-can-eat media service," Mr. Guenther said.

The business model got an endorsement of sorts this week when Next Issue Media got a new competitor: Sweden-based Readly, which also sells digital access to a collection of titles for $9.99 a month. It rolled out in Sweden in March, according to Henrik Barck, the company's co-founder. He declined to say how many subscribers the service has in Sweden.

"This is the market where we really want to focus on and be very successful," he said of the U.S.

Readly, however, has fewer titles, and it doesn't have any from the companies investing in Next Issue Media. That means some of this nation's top titles, like Cosmopolitan and Glamour, are not currently available on Readly. It does offer tablets editions from Bonnier Corp., publisher of Popular Science and Saveur magazines.

Mr. Barck said he is confident he can win over the publishers behind Next Issue Media. "We're certain we will have them in the near future," he said.

Update: Readly on Thursday night added Source Interlink magazines including Hot Rod and Powder, pushing the number of titles it offers to 137, more than Next Issue Media's 122 -- although Next Issue Media still has many more of the country's largest.