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NEW YORK — Satellite broadcaster Dish Network on Tuesday rebutted Sprint Nextel’s assertions that Dish’s offer for wireless network operator Clearwire contains illegal provisions.

Sprint, the country’s third-largest cellphone company, owns a majority of Bellevue-based Clearwire and has offered to buy out minority shareholders. However, Dish is on a quest to buy into the wireless industry, and has topped Sprint’s offer of $3.40 per share.

On Tuesday, Sprint sent an open letter to Clearwire’s board, saying the conditions of Dish’s offer for $4.40 per share are illegal and violate Clearwire’s shareholder agreement.

Dish wants three seats on Clearwire’s board and the right to veto some corporate actions, like a sale, among other provisions. The conditions would wrest rights away from Sprint, which has no intention of giving them away, Sprint said.

In a letter Tuesday to Clearwire’s board, Dish Chairman Charlie Ergen said the offer was “carefully designed to comply with applicable law and the existing rights of Clearwire stockholders including Sprint.

“We remain confident that the Dish proposal is both actionable and clearly superior to the proposed Sprint merger,” Ergen said.

Dish is also trying to buy Sprint, though Sprint has already agreed to sell 70 percent of its stock to Softbank of Japan.

Shares of Clearwire fell 11 cents, or 2.5 percent, to $4.31 Tuesday. The retreat below Dish’s offering price indicates that investors now see less chance of a substantially sweetened bid from Sprint.