WASHINGTON — In unleashing a series of punishing attacks in Gaza last week, Israel clearly aimed to hand Hamas a defeat from which it could not recover anytime soon.

The campaign may succeed, experts here and in Israel say, but it could also backfire. Either way, the political consequences could reverberate throughout the Middle East, all the way to Iran, and help determine the ability of President-elect Barack Obama to pursue his stated goals of calming the Middle East through diplomacy.

While Israeli leadership was not stating wider goals, there was clearly hope in the country — as tanks and troops massed late in the week — that the assault in Gaza would do more than just stop the rocket fire with which Hamas had broken a cease-fire last month. The larger hope was that subduing Hamas would delegitimize the group’s leadership in the eyes of the Palestinian people and eliminate its power to prevent a two-state solution. Already last week, it was exposing political, ethnic and sectarian divisions in the region that Israel, like the United States, had long sought to exploit.

In a highly optimistic scenario for Israel and the United States, a clear victory for Israel would make it easier for Egypt, Jordan and countries farther afield to declare common cause against Islamic militancy and its main sponsor in the region, Iran.

Then, as Martin S. Indyk, a former American ambassador to Israel, argued, an international peacekeeping force made up of Turkish and Arab troops could clear the way for a restoration of political control in Gaza by President Mahmoud Abbas, who heads the Fatah movement and is titular president of all Palestinians, but in reality is the weak leader of only the West Bank.

A two-state treaty could follow, and then perhaps peace between Israel and Syria, leaving Iran isolated behind the buffer of a newly democratic and peaceful, if not particularly friendly, Iraq.

Iran is the one country — aside from Israel — with the most at stake in the outcome. It sponsors Hamas and Hezbollah not only to torment Israel but also to spread its influence in the Arab world. A convincing defeat of Hamas would undercut that strategy, and presumably Iran’s ability to resist Western pressure in any broad bargaining — for example, over its support for terrorist groups and even its nuclear program. “It’s an ambitious scenario,” said Mr. Indyk, with a sobering caveat, “that would require things to get significantly worse before they could get better.”

But Israel’s attacks also could fail outright, and history suggests that as the more likely scenario, Middle East experts across the political spectrum said.

The strikes — and the Arab anger over scenes of death and destruction — have highlighted divisions in the Middle East that can prevent Arab nations from working with Israel.

Of course, Egypt, whose peace treaty with Israel is anathema to militants in the Middle East, kept its border to Gaza largely shut last week, and its president, Hosni Mubarak, quarreled openly with the leader of Hezbollah, the Iranian-backed militant Shiite group that now shares power in Lebanon. And at a meeting of the Arab League, Saudi Arabia’s foreign minister gently and indirectly rebuked Hamas for provoking the conflict. Those actions were in line with Israeli dreams. But the attacks also subjected the regimes in Egypt and other moderate Arab nations to blistering scorn from inflamed Arab populations.

And that widened the rifts between rulers and citizens in countries nominally allied with the United States and willing to deal with Israel. The longer this goes on, the more likely it is that regional tensions will intensify. The images of carnage could fuel new hatreds and radicalize some who felt that peace talks offer more hope than resistance.

In some ways, the Gaza attacks were reminiscent of the gamble Israel took, and largely lost, in Lebanon in 1982. It invaded to eliminate the threat of Yasir Arafat’s forces, which were then encamped on its northern border. It accomplished that goal, driving Mr. Arafat into exile in Tunis, and eventually he recognized Israel and negotiated. But in the meantime, a new and virulently anti-Israel threat was born in Lebanon in the form of Hezbollah. Israel’s northern border remained insecure, and Iran’s influence grew.

Now Mr. Abbas, already deeply mired in a rivalry with Hamas, could find himself further isolated from Palestinian sentiment the longer the Israeli assaults continue. Signs were growing last week that the fighting was emboldening Palestinian resistance, prompting Mr. Abbas to say he was prepared to walk away from the peace process President Bush began in Annapolis, Md., in 2007.

“What does he have to offer us a year after Annapolis?” Mustafa Barghouti, a doctor, independent Palestinian legislator and advocate of democracy, said of Mr. Abbas, in a telephone conversation from the West Bank. “They promised us an agreement by the end of the year. What do we have after this year?”

Dr. Barghouti, who was a minister in the short-lived unity government that followed Hamas’s victory in 2006 elections, said the only durable solution was an accommodation that included Hamas. “There are two ways to deal with Hamas,” he said. “Either confront them, which makes them more extreme, or accept them in the political process.”

That would hearten Islamic militants in Egypt and Jordan and make those countries’ leaders shiver a bit more; and it would very likely embolden Iran in its ambitions for regional leadership and insistence on a nuclear program.

Most analysts expect that some sort of negotiated cease-fire with Hamas is inevitable, since Israel seems neither willing nor able to reoccupy Gaza and replace its leadership. That, then, would leave the group with many followers in Gaza, even if its ranks are badly battered, its leaders driven underground and its formal centers of power, through which it might deliver services to its people, are destroyed by Israeli bombs. “Hamas as an institution is not really sustaining casualties,” said Ziad Asali, president of the American Task Force for Palestine. “The people of Gaza are the ones who are paying the price.”

Daniel Levy, an Israeli analyst with the New America Foundation here, said the flaw in the Israeli strategy is the belief that that people in Gaza will blame their own government, and not the Israelis, for the new wave of violence.

Israel, for its part, is determined to avoid the military and political catastrophe of its incursion in Lebanon in 2006 to squelch cross-border rocket attacks by Hezbollah not all that different from the ones by Hamas. That fight ended with a United Nations resolution and international peacekeepers but also, eventually, a rearmed Hezbollah.

“Israel believes its deterrence was lost in that war,” David Makovsky, a senior fellow at the Washington Institute for Near East Policy, wrote on Wednesday, “and Israel’s current campaign against Hamas should be seen as an effort to regain that deterrence.”

One lesson Israel learned from Lebanon, he argued, was to lower expectations, depriving Hamas of the chance to declare victory simply by surviving the Israeli assault, as Hezbollah did. Israel has done that by remaining vague about its final goals. Israel also seems to have prepared better; by all appearances its forces were following a methodical campaign of strikes, even as it tried to win the propaganda war — or at least to do less badly this time, by trying to minimize civilian casualties.

Almost everyone in Washington agrees that the timing of the latest crisis had at least one benefit: It came before the inauguration of Mr. Obama on Jan. 20. Although he has expressed staunch support for Israel — at one point justifying a response to Hamas rocket attacks — he has raised expectations of a change in policy in the Middle East. The fighting has certainly pushed the Arab-Israeli conflict back to the front of a United States agenda crowded with foreign crises, from Iran to India to North Korea.

It is likely that the immediate fighting will have ended by Inauguration Day. If so, President Obama will be able to capitalize on the cease-fire to renew a push for a permanent settlement. He once suggested throwing American weight behind regional talks that would include Hamas, but that may no longer be a possibility. Mr. Bush fiercely resisted any accommodation with a group the United States and European Union classify as a terrorist organization.

“He has one advantage: that this is happening now,” said Mr. Asali of the American Task Force for Palestine. “The passionate reactions, the emotional reactions, the hatred, et cetera, et cetera, will be directed at the present administration rather than the next one. But that is a slight silver lining.”