The sparring between the United States and Israel has begun, and that’s a good thing. Israel’s interests are not served by an uncritical American administration. The Jewish state emerged less secure and less loved from Washington’s post-9/11 Israel-can-do-no-wrong policy.

The criticism of the center-right government of Prime Minister Benjamin Netanyahu has come from an unlikely source: Secretary of State Hillary Clinton. She’s transitioned with aplomb from the calculation of her interests that she made as a senator from New York to a cool assessment of U.S. interests. These do not always coincide with Israel’s.

I hear that Clinton was shocked by what she saw on her visit last month to the West Bank. This is not surprising. The transition from Israel’s first-world hustle-bustle to the donkeys, carts and idle people beyond the separation wall is brutal. If Clinton cares about one thing, it’s human suffering.

In fact, you don’t so much drive into the Palestinian territories these days as sink into them. Everything, except the Jewish settlers’ cars on fenced settlers-only highways, slows down. The buzz of business gives way to the clunking of hammers.

The whole desolate West Bank scene is punctuated with garrison-like settlements on hilltops. If you’re looking for a primer on colonialism, this is not a bad place to start.

Most Israelis never see this, unless they’re in the army. Clinton witnessed it. She was, I understand, troubled by the humiliation around her.

Now, she has warned Netanyahu to get off “the sidelines” with respect to Palestinian peace efforts. Remember that the Israeli prime minister and his right-wing Likud party have still not accepted even the theory of a two-state solution.

In House testimony last week, Clinton said: “For Israel to get the kind of strong support it is looking for vis-à-vis Iran, it can’t stay on the sidelines with respect to the Palestinians and the peace efforts. They go hand in hand.”

That was a direct rebuke to comments from Netanyahu aides who told the Washington Post Israel would not move on peace talks until it sees the United States check Iran’s nuclear program and rising regional influence.

Although I don’t agree with the forms of linkage being made by Netanyahu and Clinton between Iran and an Israeli-Palestinian peace — the issue is not how to threaten Iran but how to bring it inside the tent — I agree with both of them that a link exists. At Madrid, at Oslo and at Annapolis, over a 16-year span, attempts were made to advance peace while excluding Iran. That doesn’t work; it won’t work now.

The trick is to usher Israel-Palestine peace efforts and the quest for a U.S.-Iran rapprochement along in parallel.

That’s why it’s so important that Clinton told Netanyahu that he can’t slip away from working for peace — and that means stopping settlements now — by taking an Iran detour.

Clinton also indicated an important shift on Hamas, which the State Department calls a terrorist group. While stressing that no funds would flow to Hamas “or any entity controlled by it,” she argued for keeping American options open on a possible Palestinian unity government between the moderate Fatah and Hamas.

So long as a unity government meets three conditions — renounces violence, recognizes Israel’s right to exist and abides by past agreements — the United States would be prepared to deal with it, including on $900 million in proposed aid, Clinton indicated. Washington does business with a Lebanese government in which Hezbollah controls 11 of 30 seats, although Hezbollah is also deemed a terrorist group.

Such a changed U.S. policy makes a lot more sense than the previous one, which insisted on Hamas itself — rather than any Palestinian unity government — meeting the three conditions. No peace can be made by pretending Hamas does not exist, which is why advancing Palestinian unity must be a U.S. priority.

This sensible shift will anger Israel, although it deals indirectly with Hamas through Egypt. Israel’s de jure stand on Hamas — that it must recognize Israel before any talks begin — is wildly at odds with Israel’s de facto methodology since 1948.

So it’s a week in which I cheer Clinton, although her reference to “crippling sanctions” against Iran if the proposed rapprochement fails was a mistake. Sanctions haven’t worked and won’t.

Tehran will not come to the table if it sees Obama’s extended hand as just a deceptive prelude to “crippling” measures. My advice to Tehran: watch what Obama says. He’s driving Iran policy.

Obama’s doing it in a way that means the Israeli-American friction evident in Clinton’s remarks will be a theme of his first year in office. As Lee Hamilton, the president of the Woodrow Wilson Center, told me: “Initiatives are underway that show the United States is going to have some major differences with Israel.”

He also said Netanyahu is “a little more flexible than maybe he’s given credit for.”

Netanyahu as Begin the peacemaker? It’s not impossible. Nor is Obama to Tehran. Provided the president pushes on the two fronts at once.