The Qatari ceasefire initiative, first reported by the Times of Israel Saturday, illustrates how the continuing escalation of the conflict in Gaza has actually got nothing to do with Israel itself. Unfortunately, Israel has found itself tangled up in a battle of far wider proportions — a war between two competing axes in the Sunni Muslim world.

On the one side are Egypt and the Palestinian Authority, with Jordan and Saudi Arabia likely to join them in the next couple of days. On the other, Qatar, Turkey and Hamas, as well as other global supporters of the Muslim Brotherhood.

This is a proxy war for all intents and purposes. Make no mistake, Hamas remains committed to the destruction of Israel. But Hamas is firing rockets at Tel Aviv and sending terrorists through tunnels into southern Israel while aiming, in essence, at Cairo. It is backed in this by Doha and Ankara.

What arises from this state of affairs, and from Hamas’s baseless demands as they appear in the Qatari ceasefire proposal, is that this crisis is far from over.

Hamas is confident, even euphoric. In recent days, people who came in contact with the Palestinian terror organization’s leaders report that the sense they are broadcasting is that Hamas is besieging Tel Aviv, and that it will be starting its invasion of Israel shortly, not that the IDF is striking hard at Gaza, has its ground troops hitting Hamas in the Palestinian enclave, and is setting back the Hamas terrorist infrastructure by years, as IDF Chief Benny Gantz put it on Friday night.

In a meeting with Palestinian Authority President Mahmoud Abbas in Cairo on Wednesday, Moussa Abu Marzouk, the deputy head of Hamas’s political bureau, dismissed Abbas’s pleas regarding a ceasefire, explaining that “what are 200 martyrs compared with lifting the siege [on the Gaza Strip?]” Abu Marzouk later tweeted that there will be no truce that does not acknowledge the demands of the “resistance,” and that it is “better that Israel occupy the Gaza Strip than for the siege to continue.” Abu Marzouk, needless to say, resides in Cairo, far from the threat of Israeli air strikes.

All this requires Israel to reconsider its preconceived notions and its plans of action with regard to Hamas. The basic concept that has guided Israel in recent years is that Hamas’s control of the Strip is manageable, even “good for the Jews,” and poses, at the end of the day, less of a security risk than any alternative scenario. But Israel can no longer afford to convey the message that “quiet will be met with quiet.”

Hamas has been operating under the basic assumption that Israel will ultimately work to preserve its hold on the Strip. Hence Hamas’s current confidence, even euphoria. Hamas believes Israel does not want to bring it down or to assassinate its leaders.

In order to force Hamas’s leaders to reconsider their stance, therefore, Israel had better change its tone, and fast. Hamas needs to understand that the rules of the game have now changed, and that Israel is willing to destroy it and its regime, including by seizing the entire Gaza Strip, if necessary. Tzipi Livni took a first step in that direction, to the surprise of her interviewers, when telling Channel 2 on Friday night that she did not rule out bringing down Hamas if that’s what it takes to restore sustained quiet.

This is not a recommendation for the IDF to reoccupy Gaza. But to bring an end to this conflict, Hamas must be led to believe that its demise may be just around the corner if it does not lay down its weapons. It certainly doesn’t think that now.

The Qatari ceasefire proposal sets out more or less the same terms Hamas has been demanding since the beginning of the operation, with some additional demands, including a release of prisoners freed in the Gilad Shalit exchange deal who were rearrested in the IDF’s recent West Bank sweep; the opening of the Rafah crossing; the construction of a seaport in Gaza, and more. These demands were to be met in parallel with a ceasefire.

These terms were conveyed to the American government, which was asked by Qatar to broker them with Israel. One of the goals, though not the only one, was to keep Egypt out of the ceasefire effort.

The Americans’ handling of this issue, however, was typically hesitant and unclear. Washington flirted with both Doha and Cairo. Only after Israel demanded that Qatar be removed from the picture did the US announce its support for the Egyptian initiative, with its clauses that largely ignore Hamas’s demands, and which Israel, the Arab League, the US and others quickly backed.

Qatar’s firm, ongoing support of Hamas explains its flat dismissal of the Egyptian proposal. Egypt’s Foreign Minister Sameh Shukri understood this and directly accused Doha and Ankara of attempting to deliberately undermine its ceasefire efforts. Turkey responded fiercely, with Prime Minister Recep Tayyip Erdogan calling Egyptian President Abdel-Fattah el-Sissi a dictator.

And so the Sunni war rages and the possibility of a ceasefire between Hamas and Israel becomes more remote. Abbas is still trying to bridge the gap between the parties — between Qatar, Turkey and Egypt, that is; not between Hamas and Israel. But it’s doubtful he will be the man to reunite the bitterly divided Sunni world.