The human reaction to the daily bloodshed in Gaza fills anyone who glimpses it with shock and despair. Even those who accept that Israel has a right to defend itself from incoming Hamas rockets can be appalled by the sight of a house razed by a double air strike that left, on one estimate, 22 dead and 45 injured. Afterwards, those on the ground did not deny that the Hamas-affiliated police chief of Gaza City was sheltering there, but asked why his extended family, including children, had to die too. Others ask similar questions about the target of an Israeli raid on Saturday – a home for the severely disabled. Even if Hamas was hiding personnel or equipment there, even if it was cynically using the home's disabled residents as human shields, are there not some acts which, even in the name of self-defence, exact too high a price?

These questions are pressing in on Israel now, asked even by those who are receptive to the country's core argument: that any government in the world would have to respond to rockets fired at its civilian population. Fellow governments accept that Israel has little option but to reply with force to Hamas's constant fusillade of missiles. There is an acceptance too that the Hamas arsenal is no longer the makeshift or amateurish one of old but now includes some serious firepower, capable of reaching deep into the country's most populated areas, including Tel Aviv.

The result is that you hear, in the world's foreign ministries at least, less talk now of Israel's actions as "disproportionate" than once you might. William Hague, who used the word to condemn Israel in 2006, has not used it this time. Even the most shocking fact of the past week's events – the asymmetry of the dead, which has seen more than 160 Palestinians killed, compared with no Israeli fatalities – can be understood to be chiefly a function of Israel's superior defensive infrastructure: Hamas would kill scores of Israeli civilians if it could. It's just that its missiles don't get through, while Israel's do.

And yet, for all this new understanding, a stubborn truth remains: there can be no military solution to the conflict between Israelis and Palestinians. The fact that this is the fourth such operation to quell the Hamas rockets in eight years, and that the intervals between the operations are getting shorter, underlines the point. Hitting Hamas hard does not solve the problem. It does not end the trouble. It merely brings some short-term quiet till the next eruption. Ultimately, the conflict between Israel and Hamas, and between Israel and the Palestinians, will have to be solved politically and through negotiation. There is no other way.

That, though, is the long-term objective. For now, there is a more immediate goal – an end to the bloodshed and pain. Eventually, as in each of the previous three rounds, there will be a ceasefire. So why wait? If it is due to come in a week, why endure another seven days of death? Why not cease firing now? That will require outside help. The US is wary, having seen John Kerry's peace initiative fail. But the goal now is not a grand peace treaty, just a cessation to hostilities; that cannot be beyond Washington and its European allies, even if it will require President Obama to show some steel and lean heavily on Binyamin Netanyahu.

Egypt has a role too. The new regime loathes Hamas, aligned as the latter is with the Muslim Brotherhood. It is in no hurry to help. But if President Sisi wants to win international respectability, brokering a ceasefire cannot hurt. It might also assuage some of the widespread anger among Egyptians over both the crushing of the Brotherhood and the Palestinians' plight, if he were to give Hamas a ladder to climb down. Finally, Qatar is desperate to walk tall on the international stage, buying up European property and global sporting tournaments alike. It has real leverage with Hamas. It should use that massive financial muscle for good – and do what it can to bring quiet, if not peace, to Gaza and ease the pain of those who have already suffered far too much.