The shockwaves from Israel's rampages in Gaza are having political repercussions in the tiny enclave too. Polls indicate that among a small but growing minority of Palestinians in Gaza support is shifting towards ISIS.
They blame Hamas for failing to capitalize on its relative military success last summer. Gaza is still ravaged a year on, and continuing Israeli restrictions mean the huge reconstruction project has barely begun. The people of Gaza expect their rulers to end the blockade.
Israel's recent confusing behavior in part reflects a belated realization that it needs to put out these various fires.
That explains revelations in the Israeli media that Israel is quietly cooperating with the Hague court's investigators, breaking with its past refusal to deal with international inquiries. It hopes to forestall an ICC investigation by demonstrating that it is taking action itself.
Last week Israel announced it would investigate soldiers' testimonies of war crimes collected by Breaking the Silence, a whistleblowing group that as recently as last month the Israeli government called traitors.
In addition, Neria Yeshurun has become the first senior commander to be placed under investigation, after a recording emerged in which he stated he had ordered the shelling of a Palestinian medical center to "avenge" the killing of one of his officers.
Asa Kasher, in charge of the army's code of ethics, recently argued that notorious incidents such as the massive destruction of Rafah after a soldier went missing -- the so-called Hannibal procedure that probably claimed more than 150 Palestinian lives -- reflected operational misunderstandings rather than policy. Errors, he implied, were not war crimes.
A group of Israeli military commanders have also argued that it is time to offer Gaza some relief, by easing -- if only marginally -- the blockade.
None of this is being done from conscience or out of recognition of Palestinian rights.
The moves may be conducted in bad faith but they nonetheless indicate a growing realization by some in Israel that the international community and ordinary Palestinians in Gaza need to be placated.
At the same time, according to local analysts, Israel is pursuing a dual policy towards Hamas.
On the one hand, Israel hopes diplomatic gains will bolster Hamas' political wing against more threatening newcomers like ISIS. On the other, it wishes to weaken Hamas' military wing to avoid it developing the ability to threaten Israel's control over the enclave.
As ever, Israel is keen to sow divisions where possible. The Israeli government's repeated likening of Hamas and ISIS, and the recent suggestions of military ties between the two in Sinai, are intended to remind the international community of the threat Hamas' military wing supposedly poses to regional order.
Further, it is better for Israel that Hamas commanders are forced to contend with Egypt's as well as Israel's military might, stretching it on two fronts.
Israel believes it can tame Hamas' political leadership, making them as cautious and subdued as Mahmoud Abbas' Palestinian Authority in the West Bank. But it also wants to maintain the pressure on Hamas' military wing by emphasizing that it is little different from the beheaders of Islamic State.
Israel's compulsive need to dominate Palestinians trumps all -- even as it finally dawns on a few generals that Gaza's endless immiseration is no policy at all.
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