Kansas City, Mo. ? Sprint Nextel Corp., the nation’s third-largest wireless provider, on Monday launched its downloadable music service, trying to keep up in a wireless arms race that is increasingly dominated by mobile Internet access.

The Sprint Music Store allows customers to download and play songs on specially made mobile phones, paying $2.50 for two copies of each track – one for the phone and one for a home computer.

Sprint Nextel’s announcement comes more than a month after Cingular Wireless LLC, a joint venture of SBC Communications Inc. and BellSouth Corp., introduced the ROKR handset that allows customers to play music downloaded from Apple Computer Inc.’s wildly popular iTunes store.

The Sprint Nextel phones, made by Samsung and Sanyo, can hold up to 1,000 songs with an optional 1-gigabyte memory card, 10 times the capacity of the Motorola Inc.-produced ROKR. Sprint Nextel’s library of music is more limited, however, offering more than 250,000 titles from major music labels EMI Music, Sony BMG Music Entertainment, Warner Music Group and Universal Music Group, while iTunes has more than 2 million tracks.

A Sprint Nextel spokeswoman said the number of songs would continue to increase.

Monday’s news comes as Sprint Nextel, based in Reston, Va., with operational headquarters in Overland Park, continues to ramp up its high-speed wireless Internet service, which it said should be competing nationwide with industry leader Verizon Wireless by early next year.

Currently, Sprint Nextel’s Power Vision network is offered in about 127 markets and 210 airports. By early next year, the company said it planned to offer the service, which uses EV-DO technology, in 220 markets.

Shares of Sprint closed up 6 cents at $23.25 in trading Monday.