JERUSALEM — The execution of Saddam Hussein has renewed the debate in Israel over the effect of the American invasion of Iraq on Israel’s regional position.

Seemingly, the defeat of Iraq and the toppling of Saddam’s regime should have served Israel’s deepest strategic interests. Saddam was one of Israel’s most dangerous foes. Had he succeeded in developing nuclear weapons, certainly he would have threatened Israel with them.

During the first Gulf War in 1991, Saddam showed he had the capacity to strike at Israel with long-distance Scud rockets. His army, together with those of Syria and Jordan, formed what Israeli military planners dubbed the “Eastern Front,” a potential military alliance they considered the most serious conventional threat faced by the country. And for years, Saddam was the main outside backer and financer of Palestinian suicide terror.

But there was a catch: Saddam in power also contained neighboring Iran. One of the unintended consequences of his removal has been the rise of Iran as a regional superpower, and with its advanced nuclear weapons’ program, Iran probably constitutes a greater existential threat to Israel than Saddam ever did.

There are also new potential threats to Israel from inside Iraq. As they approached Baghdad in 2003, American forces had hoped downtrodden Iraqis would welcome them as liberators from a cruel tyrannical regime. Instead, the invasion quickly unleashed bitter sectarian rivalries Saddam had been able to suppress. The result has been civil war and the virtual disintegration of the Iraqi state.

“The simplistic view that guided the American administration — that Shiites and Kurds would support the American effort and the Sunnis would be crushed — failed,” Arab affairs analyst Zvi Barel wrote in Ha’aretz.

“Each ethnic group is divided by different religious leaders, clan interests and tribal leaders,” he said.

Some Israeli analysts argue that further disintegration of the war-torn Iraqi state could have dire consequences for Israel: a breakaway Shiite state in the South could join Shiite Iran in actions against Israel and that Al-Qaida groups, allied to an unstable Sunni rump in the center, could export terror to Israel.

Others doubt it will come to that.

Giora Eiland, the former National Security Council chief, argues that the probability of a breakup of the Iraqi state is low. He says the Kurds in the North are wary of declaring independence because they know it would trigger an immediate Turkish invasion; the Shiites in the South don’t want to become an Iranian vassal state; and the Sunnis in the center, where there are few oil deposits, have no intention of cutting themselves off from the rich oil fields in the northern and southern sectors of the country.

Still, even if the Iraqi state remains intact, it is unlikely to be strong enough to serve as a counterweight to Iran.

“The vacuum created by the collapse of Saddam and the Iraqi state he headed is dangerous for Israel and the region as a whole,” Professor Eyal Zisser, a Tel Aviv University Middle East scholar, wrote in the Ma’ariv daily.

According to Zisser, Arabs critical of the Saddam execution and the American role in Iraq are not yearning for Saddam, but for the Iraq he led, “a stable country that blocked the hegemonic aspirations of the ayatollahs in Tehran.”

Echoing Zisser’s sentiments, political analyst Nahum Barnea wrote in the mass circulation daily Yediot Achronot that “Israel’s interest was that Iraq and Iran go on fighting each other forever. Saddam’s departure enabled Iran to grow to dimensions that threaten Israel’s existence and the peace of the entire region.”

Some analysts, however, point to positive developments. The rise of Iran has led moderate Arab states like Egypt, Jordan and Saudi Arabia to redefine their national interests. To curb Iranian Shiite influence, these Sunni states have grown closer to the West, and are more interested in solving the Israeli-Palestinian conflict. Israel sees them playing a central role in any future Israeli-Palestinian accommodation.

The American invasion also had positive economic consequences for Israel. If the Americans had not taken Saddam out, Israel would have had to spend billions of dollars building ground forces to check a possible Iraqi ground sweep through Jordan.

Sever Plocker, Yediot’s economics editor, observes that both American-led Iraq wars, in 1991 and 2003, were followed by economic booms in Israel. He points out that in both cases, Israel received American loan guarantees, which injected new energy into the economy.

“Israel didn’t need the money. It needed an expression of American confidence in the resilience of the economy. And like magic, after the second Iraq war, foreign investment started flowing into Israel. The stock market, as in 1991, is celebrating once again,” he wrote.

The bitter enmity between Israel and Saddam’s Iraq goes back nearly three decades. It came to a head in 1981, when Israeli jets destroyed an Iraqi nuclear reactor at Osirak, outside Baghdad. Ten years later, when American-led coalition forces attacked Iraq, Saddam fired 39 Scud rockets at Israeli cities.

In the interim, and again a few years later, secret peace feelers between Israeli and Iraqi representatives came to naught. Saddam became an active supporter of Palestinian terror, paying a reported $10,000 to every suicide bomber’s family. Palestinians generally mourned his death, eulogizing him as a great Arab patriot.

Although Israeli analysts do not believe the execution will improve things in Iraq in the short term, some argue that it could help over time.

“If Saddam had remained alive in jail, the chances of restoring calm in Iraq anytime soon would be zero,” columnist Yoel Marcus wrote in Ha’aretz. “People would be afraid that sooner or later he would get out from behind those bars and return to power.”

It is still too early to fully appreciate the regional reverberations of the American invasion. Much will depend on how the struggle between the radicals around Iran and the moderates plays out.

The American invasion opened up new challenges for Israel. But it also clarified a new lineup of regional forces, with moderate Arabs and Israel on the same side of the new regional divide.