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'Humanitarian crisis' in the U.N. statement is a specific term (I think they call such things 'terms of art'). It means a crisis that requires an intervention into an armed conflict, either passage of relief workers or supplies, or even a ceasefire. The term 'humanitarian' here is analogous to the term International Humanitarian Law, meaning the laws of war. In such circumstances a 'humanitarian' is someone who is humane, impartial, neutral, and independent -- usually marked by an acknowledged symbol (e.g. a red cross, crescent or crystal, or a U.N. flag or some other sign acknowledged by parties to the conflict) -- who must be given passage and safety to alleviate said crisis. It also implies that it is the duty of the international community to intervene if nothing else works, and that the parties to the conflict have obligations to avert or alleviate or permit such alleviation.
Whether or not war is ever humane is not relevant to that use of the term. It is assumed that the current conflict cannot be stopped in the timeframe of the humanitarian crisis and has to be accepted as the conditions under which the intervention must take place.