UPDATE 4-Sony adds wireless e-reader as Kindle rival

* Sony launches wireless digital reader

* Device costs $399, more than Sony's other readers

* AT&T to be carrier for the new device (Adds analyst comment on pricing)

By Alexandria Sage and Franklin Paul

SAN FRANCISCO/NEW YORK, Aug 25 (Reuters) - Sony Corp (6758.T) unveiled its first wireless electronic reader, challenging Amazon.com Inc's (AMZN.O) momentum in the growing digital book market.

At $399, Sony's "Daily Edition" is $100 more expensive than Amazon's basic Kindle but it has a 7-inch touch screen and an aluminum body. It will go on sale in December with AT&T (T.N) providing its 3G wireless Internet service.

After a year of headlines dominated by Amazon's Kindle reader, Sony has taken the offensive, with the wireless model joining previously announced lower-priced units.

It is unclear which consumers prefer. Amazon does not provide sales figures. In January, Sony disclosed that it had sold 400,000 readers.

Sony previously introduced the "Pocket Edition" for $199 and the "Touch Edition" for $299.