"After the skirmish on Zebes, a special corps was assigned by the Galactic Federation to destroy the Metroids on SR388. That corps was never heard from again. The Supreme Council gave Samus the job to fly to SR388 and do what the special corps could not do--make the Metroids extinct."
Because Samus was ordered to SR388 by the Galactic Federation, it can be assumed that from this information, the Supreme Council is the ruling body of the Federation. The members of the Council are unknown. Presumably, some or most are human, as most of the members of the Federation seem to in other Metroid games. It is possible, however, that individuals of other species may also be members. The council may be depicted in the Metroid Manga on Daiban with Chairman Keaton and Chairman Vogl.
This information is mostly speculative. The specific nature of the Federation's ruling body is as of yet unknown.
The Galactic Federation Council is mentioned in the introduction of Metroid: Samus Returns. It deems the Metroids too dangerous to exist and orders Samus to destroy them.