RAMALLAH, West Bank — At Tel Aviv’s Ben Gurion Airport there is a photo exhibition of great moments in Israeli airline history. One large black-and-white photograph caught my eye. It was a picture of Egypt’s President Anwar Sadat seated with Israel’s Prime Minister Menachem Begin on a flight, with both men laughing — their faces radiating friendship.

As Secretary of State John Kerry enters a key moment in his vital effort to forge a peace agreement between Israelis and Palestinians, one can’t help but be struck by how far away we are from any such photograph between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas. To say that they don’t trust each other would be a vast understatement, but without trust an agreement that will involve so many difficult, complex compromises for both sides, in such a small space, is inconceivable — as inconceivable as building a house with bricks but no cement.

I and my colleague, The Times’s Jerusalem bureau chief, Jodi Rudoren, sat down with President Abbas in his headquarters in the West Bank town of Ramallah on Saturday afternoon to probe his thinking on this issue. He returned — with greater enthusiasm than ever — to an idea whose time may have come: Summon NATO to provide the cement.

After Israelis and Palestinians agree on the contours of a Palestinian state, said Abbas, let Israeli troops remain in the West Bank for a five-year transitional period to work with Palestinian and Jordanian security forces and reassure the Israeli public that it is not going to get hit with the flurry of rockets it got hit with after Israel quit the Gaza Strip. And then have the Israeli forces replaced indefinitely by an American-led NATO force, with troops throughout the territory, at every crossing and within Arab East Jerusalem — along with, of course, Palestinian police and security units. Abbas was clearly going out of his way to show that he is prepared to go a long way to address Israel’s security concerns, but in a way that is consistent with his own sovereignty concerns.

Let NATO forces stay, said Abbas, “for a long time, and wherever they want, not only on the eastern borders but also on the western borders, everywhere ... For a long time, for the time they wish. NATO can be everywhere, why not?”

Such a force, he said, “can stay to reassure the Israelis, and to protect us. We will be demilitarized. ... Do you think we have any illusion that we can have any security if the Israelis do not feel they have security?”

Up to now Netanyahu has reportedly been demanding a very extended stay of Israeli troops in the Jordan Valley — some reports say up to 40 years — to ensure that Israel will always be able to repel any possible invasion from the east. With Lebanon, Iraq and Syria in turmoil, and Jordan under stress, Israeli officials say they cannot possibly anticipate what kind of security threats could emerge on their eastern front in the coming decades.

But Abbas says he could not possibly accept a lengthy Israeli military presence in a sovereign Palestinian state. “At the end of five years my country will be clean of occupation,” said Abbas. And that will not be based on some “performance” test scored only by Israel, he added. That would be “a humiliation for us. ... They will make a test for us and of course we will fail.”

Israel has never wanted to have American or any other international forces in the West Bank, although it has tolerated international forces in South Lebanon, the border with Syria and a U.S.-led multinational force in Sinai to monitor the Camp David peace with Egypt. Right now, even though the Palestinian security services in the West Bank have done a solid job of preventing attacks against Israel emerging from there, Israel regularly sends commando units in at night to capture or kill Palestinian militants it believes are planning violence against Israel — those whom the Palestinians cannot or will not eliminate. The Israeli Army and intelligence agencies don’t want to outsource that job, or lose that freedom of maneuver, to NATO forces, even ones led by an American general. (Kerry has proposed only a U.S. military high-tech monitoring role with sensors and satellites, but no troops on the ground.)

“The Israelis do not want the third party,” said Abbas. “[Former Israeli Prime Minister Ehud] Olmert, he welcomed this idea. Mr. Netanyahu told me directly, when we were in his house, ‘I cannot rely on anybody to protect my security except my army. ...’ He doesn’t want to leave the borders to us. I told him: ‘If you will not trust your allies, so whom do you trust? I am not bringing for you Turkey and Indonesia.’ He said, ‘I trust my army only. ...’ The Israelis are occupiers and they want to stay forever. When they say they want to stay for 40 years, it means they will not go out from our territory.”

There are many “core” issues in these negotiations — Jerusalem, refugees, settlements, border lines and recognition of Israel as a Jewish state, to name but a few. But the mother of them all — for the Israeli silent majority — is who will ensure that if Israeli forces totally withdraw from the West Bank that five, 10 or 40 years from now it won’t become a base for attacks that could close their international airport in Tel Aviv.

All one can say for now is this: There is no perfect security in this neighborhood. There will be no deal between Israelis and Palestinians if Israel insists on a lengthy stay in the West Bank. And there will be no deal if Palestinians cannot assure the Israeli silent majority that they can truly secure any evacuated territory. We have to find some overlap between these three realities and that’s why Abbas’s NATO suggestion is worth considering.

Yes, it will require Israel, the Palestinian Authority and America to all agree to do something they’ve long felt was outside their strategic comfort zones. But this is nothing. For them to strike a comprehensive peace deal on all the other core issues, they will have to leave many, many more comfort zones behind.