Bayan yakin duniya na farko, shugaban kwamitin Red Cross a filin yaki na Amurka, Henry Davison, ya ba da shawarar kafa wata hadaddiyar kungiya ta kungiyoyin Red Cross na kasashe daban daban, don ba da jagoranci a kan ayyukan ba da agaji a duk fadin duniya. A farkon shekarar 1919, an kira taron kasa da kasa kan harkokin kiwon lafiya a birnin Cannes na kasar Faransa. Taron ya tsai da kudurin cewa, don kara inganta nasarorin da kungiyoyin agaji na Red Cross na kasashe daban daban suka cimma, ya zama dole a kafa hadaddiyar kungiya ta kungiyoyin Red Cross na kasashe daban daban gaba daya. Daga baya, sabo da shigowar kungiyoyin Red Crescent na kasashen Larabawa da kuma karuwarsu, kungiyar Red Cross ta kira babban taro na uku a watan Oktoba na shekarar 1983, inda aka yanke shawarar sake sunan kungiyar zuwa kungiyar agaji ta Red Cross da Red Crescent ta duniya.

Manufar kungiyar Red Cross da Red Crescent ita ce ba da agajin ji kai a lokacin yaki da kuma kiyaye zaman lafiya ta hanyar gudanar da harkokin jin kai.