The Bureau of Interstellar Immigration is an organization that deals with interactions between Earth and extraterrestrial entities, such as Medical Mechanica. It is currently unknown if this organization is national, international or whether or not it operates in secrecy; however, seeing as it was capable of orchestrating the evacuation of Mabase, it must have some association with the governance.
The Bureau of Interstellar Immigration appears to have direct contact with Medical Mechanica, but not with the Galactic Space Police Brotherhood. The Bureau of Interstellar Immigration seems to be primarily concerned with keeping Medical Mechanica pacified, so that they don't smooth out the "wrinkles" in the minds of everyone on Earth. They come into conflict with Haruko because of her destroying of Medical Mechanica robots and her affiliation with their rival faction: the Galactic Space Police Brotherhood.
The most prominent members of the Bureau of Interstellar Immigration in FLCL are Commander Amarao and Kitsurubami. In FLCL Progressive, its main members are Masurao, Eye Patch and Tonkichi. Progressive also introduced Tami Hanae, who has experience dealing with both Amarao and current Bureau members, as well as a familiarity with Haruko dating back to the original series.