Apple Music may be gaining more paid subscribers every day, but the current king of the music streaming services - Spotify - claims that the Cupertino company is using underhand tactics to stifle the competition.

Spotify's general counsel sent a letter to Apple's lawyers this week that says the iPhone maker is "causing grave harm to Spotify and its customers" by not allowing the latest version of its app onto the iTunes store.

The letter goes on to state that Apple cited "business model rules" as the reason why it won't approve the updated app. It claims Apple is demanding Spotify reintroduce in-app billing via iTunes, which means a 30 percent commission on all subscription fees.

Spotify had been taking that extra 30 percent out of its subscribers' pockets by charging $13 per month on iOS instead of usual $10. In July 2015, the streaming company sent emails to iPhone customers urging them to sign up directly to its website and avoid the higher fee.

Late last year, Spotify ran a promotion that offered new users a three-month subscription for $0.99 if they signed up through the main site. Spotify general counsel Horacio Gutierrez says that Apple threatened to pull the app from its store if the company didn't stop advertising the offer to iPhone owners. Spotify stopped the promotion, but it also turned off the iTunes billing option in the iOS version of its app, leading to the current situation.

Gutierrez says the move is a sign of anti-competitive behavior on Apple's part.

This latest episode raises serious concerns under both U.S. and EU competition law. It continues a troubling pattern of behavior by Apple to exclude and diminish the competitiveness of Spotify on iOS and as a rival to Apple Music, particularly when seen against the backdrop of Apple's previous anticompetitive conduct aimed at Spotify [...] we cannot stand by as Apple uses the App Store approval process as a weapon to harm competitors.

At its recent worldwide developer conference, Apple revealed that developers of subscription-based apps would start getting a better deal; instead of the traditional 70/30 split, Apple's cut was dropping to 85/15. But it seems that Spotify still isn't satisfied with this.

Spotify currently has around double the number of subscribers as Apple Music. Should the dispute eventually see the app pulled from the iTunes store, it'll be interesting to see what effect it has on both services' subscriber numbers.