Sinclair Broadcast Group, the owner of the most TV stations in the country, said Wednesday it agreed to buy the Tennis Channel for $350 million, marking the local broadcast TV powerhouse’s first foray into the national cable television market.

The Wall Street Journal had first reported in September that Sinclair had been in talks for months to buy the closely held Tennis Channel, which is majority owned by private-equity firms Apollo Partners, Bain Capital Ventures, Battery Ventures, CCMP Capital and Columbia Capital. Satellite broadcasters DirecTV and Dish Network Corp. DISH -3.06% also own small stakes in the network.

Tennis Channel Chief Executive Ken Solomon will stay on, he told reporters during a conference call Wednesday.

The deal is a sign of the increasing pressure on independent cable channels like the Tennis Channel to merge with bigger players as the pay-TV distributors who carry their programming consolidate.

It also shows how a new breed of growing local TV station “supergroups” like Sinclair and Nexstar Broadcasting Group —which just landed its long-sought-after deal to acquire Media General on Wednesday—may look to diversify as they bump up against regulations limiting how many TV stations they can own.

Sinclair owns or operates 164 television stations in 79 markets, including affiliates of ABC, CBS, Fox and NBC, giving it strong leverage in negotiations with pay-TV providers for carriage fees.

This leverage will help expand the footprint of the 12-year-old Tennis Channel, which to date has largely been relegated to a sports tier on cable TV services. Already, Sinclair has struck deals that will increase the channel’s reach from roughly 30 million homes to approximately 50 million homes, the company said Wednesday.

“One of the few things that has limited our growth has been the lack of distribution that we were being afforded in comparison to our direct competitors because they were owned by larger companies,” Mr. Solomon said during the conference call. “In the world of rights acquisitions, there are limitations to where you can go when you are” a network distributed in 30 million homes, he added.

The Tennis Channel has considered a sale for some time, but was having trouble finding someone willing to pay the premium its private-equity owners were seeking. As of last fall, its owners were looking for a price north of $500 million, according to a person familiar with the matter.

Sinclair announced Wednesday that the Tennis Channel had over $200 million in net operating losses.

Sinclair’s plans to acquire a national cable channel came to light in August, in the midst of a distribution fight with Dish Network. In explaining the brief blackout that left 5 million Dish customers without Sinclair stations, Dish said it had come to terms with Sinclair on fees to carry its TV stations but the broadcaster was holding out to get distribution for a cable channel it didn't yet own.

Sinclair signaled its interest in investing in sports television in 2014 with the formation of American Sports Network, a subsidiary that syndicates high school and college sports content across both its owned stations and beyond.

Barry Faber, the executive vice president and general counsel of Sinclair, told reporters Wednesday the company first got the idea to get into the national cable network business when it purchased a bundle of local stations from Allbritton Communications that came with a Washington, D.C.-based local cable channel, NewsChannel 8. After spending “a lot of effort to try to improve that channel,” he said, Sinclair decided “it’s best for now to leave that as a local channel” and looked instead for alternatives.

Despite being “very bullish” still on the local TV station business, he said, “We are not blind to changes in the landscape…We do think there is an advantage in certain areas to being in more control of your own destiny, and being in charge of your programming.”

Write to Keach Hagey at keach.hagey@wsj.com

Corrections & Amplifications:

Sinclair Broadcast Group agreed to purchase the Tennis Channel. The headline in an earlier version of this article incorrectly referred to the buyer as Sinclair Broadcasting. Apollo Partners is one of the private-equity investors in the Tennis Channel. A previous version of this article incorrectly identified them as Apollo Global Management.