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Clearwire, the Bellevue-based wireless-network operator that agreed last month to be bought out by Sprint Nextel for $2.97 a share, received an unsolicited offer from Dish Network at a price that is 11 percent higher.

Dish bid $3.30 a share for outstanding stock in the company, which is majority-owned by Sprint, Clearwire said Tuesday in a statement.

Clearwire said its board will discuss the proposal with Dish, though it has made no decision to reconsider the Sprint offer. The deal values Clearwire at about $5 billion.

Dish, a satellite-television company that’s expanding into the mobile-phone business, aims to use Clearwire’s airwaves to bolster its wireless ambitions. As part of the deal, Dish offered to pay about $2.2 billion for 24 percent of Clearwire’s spectrum.

The transaction would require Clearwire shareholders to sell at least 25 percent of the stock and wouldn’t be dependent on Sprint’s participation.

Dish aims to provide “wireless video, voice and data the same way that we provide video,” Dish Chief Executive Joseph Clayton said Tuesday in a televised interview with “Bloomberg West.”

A complete takeover of Clearwire would be impossible, considering Sprint owns just over 50 percent of the shares, said Roger Entner, an analyst at Recon Analytics in Dedham, Mass. Dish, founded by combative billionaire Charlie Ergen, may just be trying to play the role of spoiler, he said.

“There’s no way Dish can do it,” he said. “They just want to throw a wrench in the deal. So what if they buy a portion of the shares? Sprint still owns the rest.”

Even so, Clearwire must consider the offer, said Walter Piecyk, an analyst at BTIG in New York.

“Ergen made a clearly superior offer, and Clearwire’s special committee needs to do their job and evaluate it,” he said.

The Dish offer was disclosed after the stock market closed Tuesday. Clearwire stock shot up 27 cents, or 9.3 percent, to $3.19 in after-hours trading. Dish’s offer is 13 percent above Clearwire’s closing price of $2.92 in Tuesday’s regular trading session.

“We look forward to working with Clearwire’s Special Committee as it evaluates our proposal,” Tom Cullen, Dish executive vice president of corporate development, said in a separate statement. The Englewood, Colo.-based company declined to comment further.

Sprint decided to acquire 100 percent of Clearwire in December after their four-year joint venture struggled to build a nationwide wireless network, leading to billions in losses for Clearwire.

Sprint aims to take over Clearwire’s spectrum — the airwaves that let mobile devices operate —and use it to enhance its own network. Sprint CEO Dan Hesse said last month the deal was critical to turnaround efforts at the third-largest U.S. wireless carrier.

The $2.97-a-share offer had to be approved by Japan’s Softbank, which agreed in October to buy 70 percent of Sprint for about $20 billion.

Softbank wouldn’t allow a bid above $2.97 a share, people familiar with the negotiations said at the time.

That requirement may now be put to the test if Sprint contemplates raising its bid, Piecyk said. “We continue to believe that Clearwire was a critical element of Softbank’s interest in Sprint,” he said.

Sprint, based in Overland Park, Kan., criticized Dish’s offer Tuesday and said it wouldn’t relinquish its rights as a Clearwire shareholder to allow it to be completed.

“Sprint believes its agreement to acquire Clearwire, which offers Clearwire shareholders certain and attractive value, is superior to the highly conditional Dish proposal,” the company said in a statement.

“Sprint does not intend to waive any of its rights and looks forward to closing the transaction with Clearwire and helping consumers across the country realize the benefits of this combination.”

Information from Bloomberg reporters Serena Saitto and Alex Sherman in New York, Jon Erlichman in San Francisco and Olga Kharif in Portland is included in this report.