Eminem's representatives say they should have received more compensation over National Party's copyright breach for the song Lose Yourself.
The battle over the use of the song has reached the Supreme Court, where the lawyer for American companies Eight Mile Style and Martin Affiliated said the latest decision from the Court of Appeal should have awarded additional damages for the breach.
The companies, who co-own the copyright to the song, are seeking leave to appeal a decision to lower the costs National should have to pay over the breach.
In 2017, the High Court deemed Eminem Esque, a song used in a National Party election ad in 2014, breached copyright of Eminem's song Lose Yourself.
Justice Helen Cull instructed the party to pay $600,000 to Eminem and his representatives for using the alternative version.