"The police authority believes that the principles of the issue are important and it is therefore urgent that it is examined by a higher court," the police said in a statement.
In February, Stockholm police refused to grant permission to two Quran burning attempts after far-right Danish politician Rasmus Paludan burned a copy of the Quran outside the Turkish Embassy in Stockholm in January with police protection and permission from Swedish authorities.
The police cited security concerns to block those two demonstrations.
However, the Stockholm Administrative Court reversed the decision with a ruling Tuesday, saying the cited security risks were insufficient to restrict the ability to demonstrate.