As the e-reader and tablet wars heat up, Amazon.com Inc. is launching a digital-book lending library that will be available only to owners of its Kindle and Kindle Fire devices who are also subscribers to its Amazon Prime program.

The program will be limited, at least at the beginning, in what is available to borrow. Amazon will initially offer slightly more than 5,000 titles in the library, including more than 100 current and former national bestsellers, such as Stephen R. Covey's "The 7 Habits of Highly Effective People."...