To amma a wancan lokacin kusan kasashe daban-daban suna da nasu kungiyar ta Red Cross ko kuma ta agaji, to amma an kafa asalin kungiyar Red Cross din ta kasa da kasa ne a shekarar 1919 bayan yakin duniya na farko lokacin da shugaban kwamitin Red Cross na Amurka a lokacin yaki Henry Davison ya ba da shawarar kafa wata hadaddiyar kungiya ta kungiyoyin Red Cross na kasashe daban daban don jagorantara 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. A yayin wannan taron an tsai da shawarar cewa dole ne a kafa hadaddiyar kungiya ta kungiyoyin Red Cross ta kasashe daban daban gaba daya don kara inganta nasarorin da kungiyoyin agaji na Red Cross na kasashe daban daban suka cimma, an dai ba wa wannan kungiya sunan League of Red Cross Societies. Daga baya, saboda 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 International Red Cross and Red Crescent Societies (kungiyar agaji ta Red Cross da Red Crescent ta duniya).