The rebirth of Napster last week appears to have put Apple's digital music service, iTunes, on the defensive.

Apple has issued figures claiming that users of its iTunes Music Store have downloaded five times as many songs as its newly relaunched rival.

The company said that last week its music fans purchased and downloaded 1.5 million songs during the same period that Napster 2.0 reported selling 300,000 songs.

Apple also quoted analyst Nielsen SoundScan, which reported iTunes Music Store as having more than 80 per cent market share of legally purchased downloads last week.

"During Napster's first week of operation, the iTunes Music Store sold five times as many songs as Napster did: 1.5 million versus 300,000," said Steve Jobs, Apple's chief executive, in a statement.

But Napster painted a very different picture of its first week in operation since relaunching.

"Our first week's results have quickly established the new Napster as one of the largest online music companies in the world," stated Chris Gorog, chairman and chief executive of Napster 2.0's parent company Roxio.

"Our sales have surpassed our estimates for track purchases and we significantly exceeded our plan for subscriber growth. Napster is off to a very solid start."