Yuriko Nakao/Reuters

With the help of a deep-pocketed new partner, Sprint Nextel is ready to spend money to shore up the future of its wireless network.

The telecommunications company offered on Thursday to buy out the part of Clearwire, the wireless network operator, that it doesn’t already own for $2.1 billion. The bid values Clearwire at about $4 billion.

Sprint agreed less than two months ago to sell a majority stake in itself to SoftBank, a major Japanese cellphone service provider.

Under the terms of its proposal, Sprint will pay $2.90 a share for Clearwire, according to a regulatory filing. Sprint, which already owns 51.7 percent of Clearwire, needs the approval of both SoftBank and a substantial portion of Clearwire’s minority shareholders.

Clearwire said in a regulatory filing on Thursday that its board had formed a special committee to consider Sprint’s offer.

Shares in Clearwire have slumped more than 85 percent since they began trading over five years ago. But they leapt nearly 15 percent on Thursday, to $3.16. That suggests that investors believe a higher offer may be forthcoming.

The Sprint offer could benefit both companies. For Sprint, buying all of Clearwire would lock up spectrum that Sprint could use to build out its newest data network.

Long the No. 3 cellphone service provider in the country behind Verizon Wireless and AT&T, Sprint has moved aggressively to bolster its position within a consolidating industry. Sprint’s deal with SoftBank gives it a well-heeled partner willing to infuse $20.1 billion into the company.

The Clearwire deal could also help fend off a newly revitalized T-Mobile USA, which has announced plans to merge with the smaller MetroPCS.

A deal would also give Clearwire, which has struggled for much of its existence, some much-needed cash — up to $800 million — after paying off some of its heavy debt obligations. The company reported having $1.2 billion in cash as of Sept. 30, which it expected to last about a year.

Formed with much promise as a next-generation wireless service provider, Clearwire has instead flailed after betting on WiMax, a high-speed wireless data standard that failed to gain traction.

A union of Sprint and Clearwire had long been expected. Soon after the SoftBank deal was announced, both Daniel R. Hesse, Sprint’s chief executive, and Masayoshi Son, SoftBank’s founder, intimated that acquisitions were in Sprint’s future.

“This is a scale game,” Mr. Hesse said in an interview in October.

Clearwire’s shares rose immediately after the SoftBank investment was announced, fueling speculation about a bid from Sprint. A few days later, Sprint increased its holdings in Clearwire, buying shares from Craig O. McCaw’s Eagle River Holdings. The transaction gave Sprint a majority stake in Clearwire.

Sprint is working to build out a Long Term Evolution, or LTE, network that can support the latest smartphones like the iPhone 5. Clearwire owns spectrum that is similar to the radio band that SoftBank uses, potentially creating a path for devices that can be used in both the United States and Japan.

And while Sprint has long been the biggest stakeholder in Clearwire, it hasn’t been able to exert full control over one of its most important partners.

Some of Clearwire’s smaller shareholders, including the investment firms Mount Kellett Capital Management and Crest Financial, have cautioned the company against selling out to Sprint for too low a price.

Mount Kellett has suggested that Clearwire consider selling a portion of its spare spectrum to other telecommunications companies, like AT&T or T-Mobile. And Crest Financial said on Thursday that it was willing to take steps as drastic as petitioning government regulators to block Sprint’s deal with SoftBank, in an effort to win a higher price.

An analyst at BTIG Research, Walter Piecyk, estimated that Sprint would need to pay at least $5 a share to secure Clearwire.

But Sprint already has a fair amount of leverage over its smaller partner. It already controls a majority of Clearwire’s voting shares and is its biggest customer. And having posted a string of losses, Clearwire is running out of cash to keep itself afloat.

Sprint has already been in discussions with its major partners in Clearwire — a group that includes the cable operators Comcast and Bright House as well as the chip maker Intel — to convince them that its bid represents a big premium over Clearwire’s October trading position. It is also betting that those companies are eager to shed a losing investment.

Together, they control more than 12 percent of the total votes in Clearwire. Winning them over would put Sprint significantly closer to the roughly 75 percent of the vote it will need to buy control of the company.