Probably the most interesting reaction to Hamas' victory in the Palestinian elections was one of the least noticed. It came from Essam Erian, a leading spokesman of the Egyptian Muslim Brotherhood, of which Hamas is a branch.

Erian duly lauded Hamas' "great victory." But then he added, according to a report by The Associated Press, that the Islamic militant movement should take up the challenge "of maintaining good relations with the Arab governments and world powers to secure support for the Palestinian cause."

The message from one Muslim fundamentalist to another was unmistakable: Don't be evil. Go along with the Egyptian government and the Arab League, which are demanding that Hamas renounce violence and accept previous Palestinian accords with Israel. Find a way to keep the aid dollars of the European Union and United States. No more suicide bombings.

Such rhetoric confounds the common assumption in Washington that Islamic extremists -- al-Qaida, Hezbollah, Hamas, the Muslim Brotherhood -- are merely different versions of the enemy with which the United States has been at war since Sept. 11, 2001. But Erian's words would come as no surprise to Ayman al-Zawahiri, the Egyptian who is Osama bin Laden's deputy, or Abu Musab al-Zarqawi, the al-Qaida commander in Iraq. Both recently condemned the Muslim Brotherhood, and by extension Hamas, for playing U.S. President George W. Bush's game of democracy. "How can anyone choose any other path but that of jihad?" lamented Zarqawi.

In fact, Bush's strategy of insisting on elections -- in Iraq, in Egypt, in Lebanon and in the Palestinian Authority -- has had the effect of widening a rift among the region's Islamic fundamentalists. Some, like the Muslim Brotherhood in Egypt and Jordan, have embraced democracy, and broken with the terrorists. Erian recently published an article in the Egyptian newspaper Al-Ahram defending Ayman Nour, the secular democrat who was jailed in December on trumped-up charges by the government of Hosni Mubarak. His Muslim Brotherhood won 88 seats, about 20 percent of the total, in Egypt's parliamentary elections last fall.

In Jordan, the Brotherhood, which will soon participate in local elections, helped to organize popular demonstrations against Zarqawi and al-Qaida after the bombings of three Amman hotels in November.

Hamas and Hezbollah, once firmly in al-Qaida's camp, now straddle the gap. Both movements have joined in parliamentary elections, and both have ceased acts of terrorism for the past year while refusing to give up their militias, weapons or the option of violence. Because of their participation in democratic politics, each is under unprecedented pressure to choose between Zarqawi and Erian; between pursuing an Islamic agenda by violence or by ballots.

Because Hamas is the first Sunni Islamic movement to win an election outright, its choice is particularly important: If it were to fully embrace democratic politics, the sponsors of terrorism in the Middle East -- not just al-Qaida but Syria and Iran -- would suffer a momentous loss.

It's in that light that the Bush administration watches the complex, multi-sided maneuvering that has followed the Palestinian elections. On one side stand Israeli hawks and their hard-line supporters in the U.S. Congress, who insist a Hamas-led Palestinian Authority would be "a terrorist entity," or "Hamastan," as Likud leader Benjamin Netanyahu calls it. They urge that the Islamists be prevented from taking office -- or that the Palestinian Authority be strangled if they do.

On a second side is Iran, which demands that Hamas make no concessions and offers fresh funding in the event of a Western boycott.

On a third side are Egypt and other secular Arab regimes, which support neither democracy nor Islamic movements; they'd like to make the secular Palestinian president, Mahmoud Abbas, into a strongman.

On a fourth are the Europeans, who are likely to soften their current resistance to a Hamas government, and Russia, which already has. Hamas itself is divided between hard-line outsiders, who live in Damascus on Iranian funding, and leaders in Gaza who won the elections by stumping on a moderate platform of clean government and better services.

The pitfalls here are abundant: Rob Hamas of its victory and it will return to the terrorism of Iran and al-Qaida, while the Palestinian Authority collapses. Let it off the hook and it will try to simultaneously govern and wage war on Israel, much as did Yasser Arafat.

Somewhere in the middle lies the possible outcome suggested by the Brotherhood -- a nonviolent Palestinian Islamic Cabinet that, while unready to endorse Israel, will accept existing Palestinian-Israeli agreements and the results of future elections. A peace accord would have to wait -- one was in any case most improbable -- but a foundation for the peaceful and democratic Palestinian state Bush has called for could at last be laid.

The odds are not great. Even if the Bush administration can calibrate the right mix of pressure and de facto tolerance, and get Israel to go along, Hamas might not respond. It may be, as some argue, that Islamic militants are incapable of converting to democracy as have secular terrorist movements.

But without the elections, there would be no opportunity at all.

Jackson Diehl is a columnist at The Washington Post, where this comment first appeared.