The race is now on between Apple and Napster to take on the largely untapped Japanese digital music market.

Napster on Wednesday announced a partnership with Tower Records Japan to bring a version of its music store to the country within one year. So far, Napster has opened music stores in the U.S., U.K., and Canada, with plans to launch in Germany in the coming months.

Napster is far behind market leading iTunes, which now has 19 international stores including the United States.

According to recent reports, Apple is planning to launch a localized version of the iTunes Music Store in Japan sometime this month, however the intricacies of the Japanese market pose problems for both operators.

Japanese analysts say there is practically no market for downloading music to PCs. But there is a $190 million market in downloading songs to mobile phones, something neither music store currently supports.