Clearwire Corp.’s board agreed Monday  to a sweetened, $2.97-a-share takeover bid from its wireless partner Sprint Nextel Corp., which is now offering $2.2 billion to acquire the portion of the company it doesn’t already own.

The new offer was approved by Japan’s Softbank Corp., which agreed in October to buy 70 percent of Sprint for about $20 billion, the companies said today in a statement. The bid also has the backing of Clearwire’s strategic investors such as Comcast Corp. and Intel Corp.

Sprint is moving to acquire 100 percent of the company 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 bolster its own network. Sprint Chief Executive Officer Dan Hesse said Monday that the deal is “critical” to turnaround efforts at the third-largest U.S. wireless carrier.

“Strategically this is a good move for Sprint,” said Joe Bonner, an analyst at Argus Research in New York. “Clearwire was a never-ending source of problems, and Softbank has the deep pockets to get it done.”

Clearwire fell 14 percent to close at $2.91 in New York. Shares of the Bellevue, Washington-based company closed at $3.37 at the end of last week, signaling that investors had expected a higher bid. Sprint rose 0.2 percent to $5.56.

The deal would give Sprint control of a flailing affiliate, one it depends upon to provide high-speed “Sprint 4G” data services on some of its phones. It would increase Sprint’s access to the airwaves, meaning it could boost data speeds in coming years. However, cell towers using Clearwire spectrum have poor range, making it difficult to provide broad coverage.

A majority of Clearwire’s minority shareholders need to approve the deal. Of those, cable companies Comcast Corp. and Bright House Networks, as well as chipmaker Intel Corp. have agreed to vote in favor. They control 13 percent of the shares.

Analyst Christopher King at Stifel Nicolaus said it’s likely other shareholders will oppose the deal, arguing that Clearwire is worth much more. That means that final approval “may come down to a vote-counting exercise,” he said.

On a conference call, Clearwire CEO Erik Prusch defended the deal, saying that since Sprint was not interested in selling its stake to another company, it was the only possible buyer. Without a deal, the company may have had to give its debtholders control, wiping out the shareholders, he said.

Clearwire was formed by cellular pioneer Craig McCaw to take advantage of an emerging wireless technology, WiMax, which promised higher speeds and lower costs than conventional cellular technology.

Sprint was working on the same technology. In 2008, it rolled those operations into Clearwire, gaining a stake of more than 50 percent. Sprint pays Clearwire for access to its network, which it resells as Sprint 4G, but the technology has been orphaned as other wireless carriers have opted for another fourth-generation technology called LTE. Sprint is now building out its own 4G LTE network. Clearwire has its own plans to build out LTE, but has lacked the funds to do so — Sprint is its only major customer.

Sprint was also financially strapped, until it agreed in October to sell 70 percent of itself to Softbank Corp. of Japan for $20 billion. Clearwire shares nearly doubled in value when that deal was announced two months ago, as investors guessed that the Softbank deal meant Sprint would buy full control of Clearwire.

Sprint’s $2.97-per-share offer for Clearwire is more than twice the stock’s closing price of $1.30 on Oct. 10, just before the Sprint-Softbank deal was confirmed.

(Bloomberg and The AP contributed to this report.)