As President Obama was arriving in Cairo on Thursday to urge the Middle East toward peace, Hamas militants in the West Bank city of Qalqilya were fighting a gun battle against Palestinian Authority forces in which three men were killed. Israel Radio was reporting that settler extremists had sent letters to an Israeli general threatening him and his children, and comparing the forces that remove settler outposts with the Jewish councils obliged to collaborate with the Nazis.

No matter how seriously and intelligently Mr. Obama presses Israel and the Palestinians to make peace with each other, little is likely to be accomplished until something else is addressed: the fierce and explosive divisions within each society between those who favor a deal and those who oppose one.

As Yisrael Wolman, an editor at the newspaper Yediot Aharonot, wrote, “It isn’t clear whether the new American administration’s aggressive initiative will promote the prospects of peace in the region, but it will undoubtedly lead us quickly to an ugly confrontation within Israel.”

In truth, such a confrontation is always just below the surface in both societies, rearing up when compromise in the name of coexistence is placed on the agenda. This is because, despite Mr. Obama’s assertion that all sides would benefit from peace, the idea of a win-win outcome is foreign to the tribal mentality. In this region, when you win, your opponent loses.

Shimon Peres, Israel’s president, was foreign minister in 1993 when Israel and the Palestine Liberation Organization reached agreement in Oslo for mutual recognition and peaceful coexistence. Two years later, as efforts to put the agreement into effect were faltering, Mr. Peres told a small group of foreign correspondents that the challenge of making the accord work was heightened by the fact that only half of one nation had decided to seek peace with half of the other, which made disruption easy.

Oslo is now widely viewed by both sides as a failure. Since Mr. Peres’s comment, the poll numbers have shifted. Sometimes more and sometimes fewer than half favor a deal, generally defined as a two-state solution. But whatever the proportions — it depends greatly on how the question is phrased and on what atrocity recently occurred — a substantial part of each society so deeply mistrusts the other that it can fight off an accord. Many Israeli governments have fallen over the issue.

There are striking parallels between the hard-core opponents of a peace deal on each side. They are generally driven by a belief in a law higher than any created by human legislatures; they are exceptionally motivated; and they are very well organized.

“It is the religious fervor that makes the anti-peace camp so much more effective and better organized on both sides,” said Yossi Alpher, the Israeli co-editor of bitterlemons.org, a Web site devoted to Israeli-Palestinian dialogue, and former director of a strategic studies center at Tel Aviv University. “Look at how settlers go to wealthy Jews and evangelical Christians to raise money and how Hamas taps into a huge reservoir of Islamist money.”

While those who lead the struggle against any peace deal are rebels, those who promote coexistence seek normality, and are loath to engage in tire burning or disruptive protests. This puts them at a disadvantage.

There is another parallel. Both Zionism and Palestinian nationalism were born in the fight against foreign rule. The Zionists rebelled against the British through surreptitious immigration and settlement as well as armed struggle. The Palestinians have, of course, been fighting the Israeli occupiers. One result is that among each society’s greatest heroes are violent lawbreakers who stood up to power. Expunging the message that defiance of the law is worthy of honor has been a challenge. West Bank settlers have something in common with the Zionist settlers of a century ago. They plant facts on the ground, often over the objections of the official authorities.

Among Palestinians, the problem is worse. Hamas has risen markedly in popularity and power, while the power of Israel’s religious parties has stayed relatively constant. Still, because of the Israeli political system, the power of the religious right has been disproportionate, as it is in the government. “They punch above their weight politically,” noted Gerald Steinberg, chairman of the political science department of Bar Ilan University. “And by threatening and using violence, a small percentage of settlers have power in great disproportion to their numbers.”

Mr. Steinberg rejected what he called an “artificial symmetry” between the peace opponents in Israel and among the Palestinians, saying 15 percent of the Israeli public opposed a deal on ideological grounds whereas the percentage was much higher among Palestinians — possibly the majority, given the strength of Hamas.

There has been a growing disillusionment in Israel with peace negotiations, he said, but he traced it to a practical concern, not ideology. The concern, he said, is that the Palestinians could not live up to a deal because of their own internal disputes and the power of Hamas. In addition, the rise of Iranian influence in the region makes Israelis fear that withdrawing from occupied land brings Israel within rocket range of hostile forces that might not let the Palestinians live in peace with Israel, even if they wanted to.

The Palestinians point to four decades of settlement building and military actions like the offensive in Gaza in January as evidence that Israel is not serious about two states. Meanwhile, internally they are more fissured than ever. Not only are they divided between Hamas rule in Gaza and Fatah domination in the West Bank, but divisions are deep within Fatah.

“Fatah follows an old Soviet style of a politburo, trying to make consensus decisions, which has been a total failure,” a Western democracy trainer who has worked with Fatah for four years argued. He insisted that his name not be used so he could speak openly about a group he works with.

Moreover, he said, the unity talks between Fatah and Hamas in Cairo are part of a double game. The Palestinian president, Mahmoud Abbas, privately opposes reconciliation, preferring the defeat of Hamas, yet he sends negotiators, ostensibly to cut a deal.

A poll last week carried out by the Palestinian Center for Policy and Survey Research found that most Palestinians have no faith that the two movements will reconcile, and a majority say they are worried that they or a member of their family will be hurt by other Palestinians.

Meanwhile, the Israeli government has vowed to dismantle illegal settler outposts, but a group of right-wing rabbis has called on Israeli soldiers and policemen to defy any removal order.

The statement called the government’s decision to enforce Israeli law through such removals, “an act that will widen further the schism between the people and the army.” Should Mr. Obama ultimately have his way, with a Palestinian state planned for the areas where those settlers live, that schism could turn into a chasm.