Napster has claimed that the injunction served last week to close it down violates its rights to free speech.
The music file-trading service has requested that a federal appeals court reviews the decision, which was taken after a three-judge bench ruled Napster was infringing copyright.
Napster filed its request last Friday. The company also argues that the court ruling thwarts new technological development.
Napster will remain open until at least 2 March, when a hearing will be held to determine the terms of the injunction.
Last week, Napster asked the Recording Industry Association of America to dance to its tune in a deal worth $1 billion, but the bid failed to attract the response the company had hoped for.