The crisis resolution required a game changer, an unimaginable volte-face. My proposal to Prime Minister Benjamin Netanyahu was to release Sheikh Ahmed Yassin, the quadriplegic founder and leader of Hamas, as a token to King Hussein. Netanyahu rejected my suggestion as “impossible” on Sept. 26 — and then hastily adopted it the following day. Thus was the probable suspension by Jordan of the peace treaty with Israel averted.

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As it happens, the current situation has deteriorated even as the state comptroller released a report on the 2014 war between Israel and Hamas. It cites the total absence of consideration of political options as alternatives to what Israel called Operation Protective Edge, the military incursion that has neither afforded long-term “protection” nor affirmed any “edge.”

That was the latest of three major Israeli attempts in the last 10 years to change the status quo in Gaza, all of which have ended in what has been described as “deterrence” of Hamas, but in practice has been mutual deterrence. Can we reset this march of folly?

Back to my audience with King Hussein. He had sent the Mossad, Israel’s spy agency, an oral message on behalf of Hamas offering a kind of armistice with Israel, potentially extending for decades, about a week before the botched assassination attempt. The Mashal operation was perceived as a direct reaction to that. In fact, nobody on the Israeli side had thought the Hamas offer worthy of response — nobody in the Mossad even vaguely entertained sending it to the political level for consideration. King Hussein was a veteran in the practice of how to keep deadly enemies at bay, and he used the occasion to impart some of this wisdom to me.

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In the 20 years since we spoke, we have seen the Second Intifada (2000-2005) with more than 1,000 Israeli deaths and over 6,000 wounded as well as more than 4,000 Palestinians dead and 30,000 wounded; a withdrawal of Israel from Gaza and the northern part of the West Bank; and the three inconclusive campaigns against Hamas in Gaza. Yet the political level in Israel is still refusing to allow attempts to begin a dialogue with Hamas because, it is said, it has blood on its hands and continues to advocate the destruction of Israel.

The state comptroller quotes Netanyahu as saying there is no sign that Hamas is changing its policy toward Israel. Officially this is true. On the other hand, Hamas leaders have expressed themselves in private to high-level former political figures and former diplomats in very different terms. I know this for a fact.

The international contacts of Hamas are growing. At the end of the last Gaza war, Russian Foreign Minister Sergey Lavrov met Mashal in Doha, Qatar, and invited him to visit Moscow. Mashal is leaving the position of head of the Hamas political bureau and is a serious candidate to succeed Mahmoud Abbas as president of the Palestinian Authority.

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There remains no good case for Israel to shun Hamas. Israel rightly prides itself as one of the strongest powers in the Middle East, but it will gain nothing from yet another round of fighting. Game changers must come from those who have the upper hand.

If the United States coaxes Israel in this direction, Washington could benefit greatly and even enlist Moscow as an interested party. If on the other hand Israel opts once again to turn a deaf ear to the drums of war and fighting breaks out, Israel alone will “own” the result. Nobody will expend funds and political clout on behalf of Jerusalem — and the United States will be unable to save its ally from its own deeds and misdeeds.