Sprint Nextel Corp. offered to take over its Clearwire Corp. in a $2.1 billion deal, ending a four- year joint venture that struggled to build a nationwide network capable of challenging Verizon Wireless and AT&T Inc.

Sprint, which already owns more than 50 percent of Clearwire, is seeking to acquire the remaining shares at $2.90 each, according to a regulatory filing today. That’s 5.5 percent more than the stock’s closing price in New York Wednesday. Sprint proposed to provide interim financing of as much as $800 million to help keep the money-losing Clearwire afloat.

Clearwire Corp. stock is up 27 cents, or 10 percent, to $3.02 in premarket trading.

Sprint uses Clearwire’s network to provide “Sprint 4G,” but it’s building its own 4G network at the same time, and would like to see Clearwire upgrade its network to use a compatible technology. Clearwire is strapped financially, and lacks the funds for a comprehensive upgrade.

Sprint, the third-largest U.S. carrier, is getting an influx of cash from Japan’s Softbank Corp., which agreed in October to buy 70 percent of Sprint for about $20 billion.

While Clearwire never broke even, it owns a broad swath of airwaves across the country. That would give Overland Park, Kansas-based Sprint the ability to improve its own network and handle a surge of traffic generated by smartphones and tablets.

“Clearwire’s got a tremendous asset in deep spectrum, and we think Sprint would like access to that,” Jonathan Schildkraut, a New York-based analyst with Evercore Partners Inc., said before the Clearwire offer was announced.

Sprint formed the Clearwire joint venture in 2008, relying on $3.2 billion in investments from Google Inc., Intel Corp., and cable companies such as Comcast Corp. and Time Warner Cable Inc. The idea was to build a high-speed wireless network that would shake up the telecommunications industry and allow for a wave of new applications and devices.

Clearwire never lived up to its original ambitions, and the costs of the project led to billions of dollars in losses. The Bellevue, Washington-based business also relied on a technology called WiMax that was later overtaken by LTE, or long-term evolution, now the industry’s preferred standard. Along the way, partners such as Google and Time Warner Cable sold their stakes for a fraction of their original value.

(Bloomberg and The AP contributed to this report.)