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Smartphones, tablets and computers all pull data from the Internet, but people still pay two different bills: the high-speed connection they get at home and the wireless connection they get outside. Dish Network, the pay-TV operator, wants to bridge that gap.

Dish Network said on Monday that it had submitted a $25.5 billion bid for Sprint Nextel, the nation’s third-largest wireless carrier after Verizon Wireless and AT&T. It says that a merger between the two companies could roll television, high-speed Internet and cellphone services into a single package that would be faster and more affordable for consumers.

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“It really means that we’re going to give consumers what every consumer wants,” Charles W. Ergen, Dish Network’s chairman, said in a phone interview. “They want broadband and video and voice in their home and want the exact same thing outside the home. And they want it to look and feel and priced outside the same as it is inside.”

Dish Network’s bid is an effort to scuttle the planned takeover of Sprint Nextel by the Japanese telecommunications company SoftBank, which agreed in October to acquire a 70 percent stake in the American cellphone operator in a complex deal worth about $20 billion.

Under the terms of its proposed bid, Dish Network said it was offering a cash-and-stock deal worth about 13 percent more than SoftBank’s bid.

Dish Network values its offer at $7 a share, including $4.76 in cash and the remainder in its shares. The offer is 12.5 percent above Sprint Nextel’s closing share price on Friday.

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“The Dish proposal clearly presents Sprint shareholders with a superior alternative to the pending SoftBank proposal,” Mr. Ergen said in a statement.

Mr. Ergen said a “Dish/Sprint merger will create the only company that can offer customers a convenient, fully integrated, nationwide bundle of in- and out-of-home video, broadband and voice services.”

Dish Network said it would be able to combine its existing broadband and TV offerings with Sprint Nextel’s cellphone operations, allowing it to better compete with rivals like Verizon that are moving into new areas in search of revenue.

Dish Network’s effort to take over Sprint is the latest of many moves toward consolidation in the highly competitive broadband industry. In 2011, AT&T tried to buy its rival T-Mobile USA, a move that was blocked by the Justice Department because of antitrust concerns. Last year, Verizon scored a deal with a group of cable companies that agreed to sell it spectrum licenses to build its wireless network in exchange for allowing them to sell their cable services inside Verizon stores.

The big question surrounding the communications industry is whether partnerships and mergers are good not just for businesses, but also for the customers. Opponents of mergers say they lead to fewer jobs, less competition and higher prices. But analysts on Monday said that a potential Dish-Sprint merger may pose a greater challenge to AT&T and Verizon, which dominate the wireless industry and charge higher prices for their phone plans.

As the No. 3 cellphone service provider, with 56 million subscribers nationwide, Sprint Nextel has struggled to catch up with larger rivals. It is expected to face even more competition as the parent company of T-Mobile USA, Deutsche Telekom, moves closer to a multibillion-dollar agreement to buy MetroPCS.

Dish Network said it would finance the cash component of the takeover through a combination of $17.3 billion in cash and debt financing.

Sprint said in a statement that it would look at Dish’s proposal, but declined to comment further on its plans. “Sprint Nextel today confirmed it has received an unsolicited proposal from Dish Network to acquire the company,” said Roni Singleton, a Sprint spokeswoman. “The company said that its board of directors will evaluate this proposal carefully and consistent with its fiduciary and legal duties. The company does not plan to comment further until the appropriate time.”

Mr. Ergen said his company would be as a better fit for Sprint than SoftBank because it would bring greater benefits to consumers. Fourteen million Dish Network subscribers would get improved services on their cellphones, and shareholders would own 32 percent of the combined company, whereas Softbank’s merger is essentially a cash infusion to strengthen Sprint.

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“Sprint doesn’t change overnight because of SoftBank — it’s still Sprint,” he said. “Sprint transforms overnight with Dish.”

Susan P. Crawford, a law professor at Cardozo School of Law who served as special assistant to President Obama for science, technology and innovation policy, said there were pros and cons to a merger with Dish Networks. A combination with Dish Networks would pose more of a threat to AT&T and Verizon, which account for two-thirds of American wireless subscribers, than a partnership with SoftBank, she said.

But it would also weaken T-Mobile USA, the No. 4 carrier, which has been offering cheaper phone plans to consumers, like its latest contract-free phone plans.

“Right now, we have two giants and two also-rans, and now you’re getting potentially three giants dividing up the American marketplace, with T-Mobile lagging far behind,” she said of the potential Dish-Sprint merger.

It is unclear whether a Dish takeover would change much about Sprint’s wireless service. Chetan Sharma, an independent telecom analyst who is a consultant for carriers, said that the only obvious change for consumers would be at a marketing level, not a technology level. While the bills may be consolidated, it would not be easy to share the benefits of a high-speed Internet connection at home with wireless networks that connect to a phone outside, he said.

Mr. Sharma said that a Sprint merger with SoftBank would most likely be better for consumers than one with Dish. The two carriers combined would have more buying power to negotiate with manufacturers like Apple or Samsung to buy large quantities of phones at lower prices.

Because the phones would be cheaper for Sprint, the carrier could charge customers less for access its network to make up for the costs of the phones, he said.

Amid the fight for Sprint is a tug of war for Clearwire, another wireless operator of which Sprint is the majority owner. Sprint has signaled interest in taking over the company entirely with the cash infusion from SoftBank, but Dish in January made an unsolicited bid of $2.2 billion for a portion of the company.

And on the heels of Monday’s news, Verizon offered $1.5 billion to buy spectrum from Clearwire, according to a person briefed on the company’s plans, who was not authorized to speak publicly because the plans were not yet official.

If Dish Networks succeeded in a takeover of Sprint, it would be in a position to acquire Clearwire more quickly than Sprint/SoftBank, because a foreign company that tries to buy more than 25 percent of a telecom company must undergo regulatory review.

Barclays is advising Dish Network on its proposed bid. Deutsche Bank, the Raine Group and Mizuho Securities are advising SoftBank. Citigroup, Rothschild and UBS are advising Sprint Nextel.