He said that, in the end, his conscience and instinct told him that if these themes were "too grave and complex" to be addressed in concert, "then it is also quite impossible to look the other way".
Costello said he was equally aware of the sensitivities behind those themes and "of so many despicable acts of violence perpetrated in the name of liberation".
He apologised to fans and also many in the Israeli media who he said had helped him to gain an understanding of the cultural scene there.
Costello said he regretted the fact that he probably would not receive another invitation to play in Israel, but imagined "a better time" when he would not be writing such a statement.
He joins other performers including Gil Scott-Heron and Santana, who have dropped tours in Israel in recent months.