Britain in January became the first country officially to recognise Parkour, which was founded in France in the 1980s and takes its name from the French word 'parcours' (course or route).
In an open letter to the International Gymnastics Federation (FIG), Parkour UK emphasised that it was a "distinct and unique sport in its own right and not a discipline of any existing sport/activity.
"Parkour/Freerunning is not 'gymnastics', nor are Traceurs/Freerunners 'gymnasts'," it added. "We are our own sovereign sport with independently recognised distinct uniqueness and cultural status."
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The FIG executive committee had said in a statement in February that it agreed the development of a new discipline aimed at broadening the appeal of gymnastics after research into parkour.
Parkour UK called for a meeting with FIG to agree a memorandum of understanding and said it would take any dispute to the Court of Arbitration for Sport.
(Reporting by Alan Baldwin, editing by Neil Robinson)
