By ELLIOTT ABRAMS

The sky is not falling. Israeli-Palestinian peace negotiations were suspended on Sunday, perhaps briefly and perhaps for months, after Israel’s 10-month moratorium on settlement construction expired. Palestinian officials said they would refuse to talk if construction restarted, and so they did. Yet war hasn’t broken out, nor will it.

Terrorism exploded after the Camp David talks broke down in 2000 because the Palestinians’ leader at the time, Yasser Arafat, supported it. Fortunately, those days are gone. As current Palestinian Prime Minister Salam Fayyad told Jewish leaders in New York last week, violence “has to be dealt out of the equation permanently regardless of what happens in the peace process.”

Also last week, Palestinian President Mahmoud Abbas reminded his people that “we tried the intifada and it caused us a lot of damage.” Hamas, the terrorist group that rules the Gaza Strip, can commit acts of terror at any time. But with Israeli and Palestinian officials working together to keep the peace, Hamas can’t create a general uprising.

Peace negotiations between Israel and the Palestine Liberation Organization (PLO) have been an on-again, off-again affair since they began with the Oslo Accords in 1993. During the Arafat years talks alternated with terrorism, for Arafat viewed both as useful and legitimate tactics. After the so-called second intifada of 2000-2001 and the 9/11 attacks, Israel’s then-Prime Minister Ariel Sharon ran out of patience with that game, as did President George W. Bush. From then on they worked to push Arafat aside.

After Arafat’s death in November 2004, negotiations between Israel and the PLO were almost continuous—until 2009. They broke down when the Obama administration made settlement construction the central issue, declaring that it had to stop dead for peace talks to proceed. Mr. Abbas, who heads both the Palestinian Authority and the PLO, could not allow President Obama to take a harder line than his own, so he echoed the demand.

Why Mr. Obama felt it necessary to raise this issue is unclear, for it had successfully been put aside during the Clinton and Bush years. Settlements grew steadily in the 1990s despite the Oslo peace process. Under Mr. Bush, an arrangement was reached whereby the Israelis would build inside settlements but not expand them physically.

The Obama administration junked that deal, and its continuing obsession with a settlement freeze—Mr. Obama mentioned it again at the U.N. last week—has cornered Mr. Abbas. The Americans are effectively urging him back to the table while making it impossible for him to get there. This diplomatic problem is what medical science calls “iatrogenic”: a disease caused by the physicians themselves.

Faced with this situation, Mr. Abbas has once again decided to hide behind the Arab League. When Arab foreign ministers next meet, on Oct. 4, he will seek the league’s cover—and public support—either for continuing to refuse talks or for returning to the table.

This is where American influence should be focused now: on getting the Arabs to give Mr. Abbas the green light. As for the Israelis, Prime Minister Benjamin Netanyahu is trying to find a middle path. He won’t renew the moratorium, but he has asked settlers to act with “restraint and responsibility.” That seems to mean that construction—and publicity surrounding it—should be limited.

The good news is that while settlements capture headlines and excite diplomats, back in the real world progress is being made. The World Bank reported this month that “If the Palestinian Authority (PA) maintains its current performance in institution-building and delivery of public services, it is well-positioned for the establishment of a state at any point in the near future.” The West Bank’s economy will grow 8% this year, said the bank. Meanwhile, tax revenues are 15% above target and 50% higher than in the same period last year.

Regarding security, cooperation between Israeli and PA forces has never been better. This month the International Crisis Group acknowledged that “In the past few years, the Palestinian Authority (PA) largely has restored order and a sense of personal safety in the West Bank, something unthinkable during the second intifada. Militias no longer roam streets, uniformed security forces are back, Palestinians mostly seem pleased; even Israel—with reason to be skeptical and despite recent attacks on West Bank settlers—is encouraged.”

Most of this good news came, of course, during 18 months when there were no peace negotiations at all.

This week’s suspension of talks will be dangerous only if it interferes with this progress. A Palestinian state must be built on the ground in the West Bank, not at a conference table in Oslo, Camp David or Annapolis.

Both sides want negotiations and sooner or later will find their way back to them. But Israelis and Palestinians could more easily find compromises if American officials would be pragmatic and stop mentioning a freeze in every speech.

Mr. Netanyahu, for his part, could further improve conditions in the West Bank by removing additional checkpoints that limit Palestinian mobility more than they help Israeli security. Mr. Abbas could receive the Arab League’s blessing to return to talks, even if “temporarily” or “conditionally” at first. And both could agree on some limits on settlement construction. All sides would explain that there are other important issues—refugees, borders, security—on the table, and they want to dig into them.

This will happen eventually. How long it takes depends largely on when American officials stop obsessing over settlements.

Mr. Abrams, a senior fellow for Middle Eastern Studies at the Council on Foreign Relations, handled Middle East affairs at the National Security Council from 2001 to 2009.