Director general Mark Thompson has said by airing the appeal the BBC would risk reducing public confidence in its impartial coverage of the conflict.
Sky News has similarly declined to show the appeal, also citing incompatibility with its objective coverage of the conflict in Gaza.
Politicians have urged a review of the BBC's decision, and a crowd of 2,000 protested outside the BBC's London HQ.
We do want to cover the humanitarian story, we want to cover it in our news programmes where we can put it in context, we can do it in an even, carefully balanced, objective way.
We worry about being seen to endorse something which could give people the impression that we were backing one side. "