WASHINGTON – The killing of powerful Iranian military leader Qasem Soleimani prompted fears of violence and chaos across the Middle East as national security experts warned it could galvanize Iran's proxy forces against the United States and put a target on Americans across the globe.

Already, Iran has threatened "revenge," world leaders have expressed alarm, and Secretary of State Mike Pompeo has been working the State Department phone lines to reassure and rally unnerved American allies. Soleimani led Iran's elite military force and was the country's second most influential figure.

"The entire world will need to be on high alert for months or, more likely, years," said Jon Alterman, senior vice president of the Center for Strategic and International Studies and an expert on global security.

Iran will respond by "forcing itself to the forefront of U.S. foreign policy considerations for years to come and drawing the United States into precisely the sort of shadowy battles the Pentagon has been trying to escape for more than a decade," Alterman said in a CSIS analysis posted Friday.

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Pompeo insisted the U.S. airstrike would make Americans safer, reduce Iran's influence across the Middle East and lessen tensions.

But that view was not widely shared as policymakers in the U.S. and across the world came to grips with the Trump administration's surprise decision to launch the strike, which killed Soleimani on Iraqi soil. The attack came after a months-long tit-for-tat escalation between the U.S. and Iran, with the latest episode unfolding earlier this week at the U.S. Embassy in Baghdad when pro-Iranian protesters stormed the compound.

Now, despite President Donald Trump's promise to pull back from far-flung military engagements, he has ordered another 3,000 American soldiers to the Middle East. Many fear they will be drawn further into costly and hard-to-win conflicts across the region.

"I fear we’ve lit a fire without an extinguisher on hand," said Benjamin Friedman, policy director for Defense Priorities, which advocates restraint in U.S. military policy.

Whether Thursday's attack will lead to a full-blown war with Iran, or a shadow conflict waged by Iran's proxy forces, is not clear.

"Trump talks about ending the endless wars and leaving the Middle East. In reality, he may have just started another endless and unwinnable war and ensured that America will remain trapped in the Middle East for decades to come," said Trita Parsi, an Iran specialist and executive vice president of the Quincy Institute for Responsible Statecraft, which advocates diplomacy over military engagement.

But Parsi said proxy forces Soleimani nurtured into lethal militias from Syria to Iraq may pose the biggest risk for the U.S. Those groups aren't always under Tehran's direct control, "so even if both Washington and Tehran seek de-escalation, they may not be able to ensure that others don't add fuel to the fire," Parsi said.

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Iran saw Soleimani as 'untouchable'

Mark Dubowitz, chief executive of the Foundation for Defense of Democracies, a Washington-based research institute that supports a hardline on Iran, said he would "never discount the possibility of war," but Iran is more likely to opt for a less dramatic, if still forceful, response.

"They do not want to confront the United States military," he said. And Iran's leaders are reeling from Thursday's attacks, shocked by Trump's willingness to authorize such a bold operation.

"They thought Soleimani was untouchable and he operated in that kind of brazen way," he said.

Soleimani's playbook, Dubowitz noted, had been to use its proxy militias and radical cells to "inflict as much damage" as they can on U.S. interests and allies, without leaving too many fingerprints.

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'First and foremost': Threats to Americans in Iraq

Dubowitz and others said Iraq is likely to bear the brunt of the revenge Iran vowed. The Iranians already have militia groups there, and Iran wields political influence there as well. Some Iraqi leaders are already clamoring for U.S. accountability – and the end of America's military presence in Iraq – in the wake of Thursday's attack, which occurred at Baghdad's airport.

"The smartest play for them is not to kill Americans but to drive us out of Iraq," Dubowitz said. "I think that would be the fulfillment of Soleimani's lifelong ambition."

But others said Americans in Iraq, and elsewhere in the region, will almost certainly be targeted and drawn into the violence. Friedman noted the U.S. strikes killed not only Soleimani, but also Abu Mahdi al-Muhandis, an Iraqi who served as the deputy commander of an Iran-backed militia organization known as the Popular Mobilization Forces.

"He's a high-ranking guy in Iraq who has a lot of well-armed people who reported to him," Friedman said.

He and others said American troops and diplomats stationed in Iraq are now extremely vulnerable to attacks from Iranian-backed militia groups operating there.

"First and foremost this involves threats to the American Embassy in Baghdad, to American military personnel in Iraq, and civilians in Iraq," Thomas Warrick, a senior fellow at the Atlantic Council think tank and a former counter-terrorism official with the Department of Homeland Security, said during a conference call on Friday.

That's why the State Department issued an alert Friday advising all American citizens to leave Iraq immediately, Warrick said.

He said Iran is likely to retaliate against the U.S. but not with a military strike.

"It would not surprise me if Iran was trying to carry out cyber-attacks against US targets right now," Warrick said. He added that while Iran's ability to carry out quick, large-scale military attacks is limited, the country's cyber capabilities have "increased enormously" over the past decade.

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Pompeo: World is a 'much safer place'

Kirsten Fontenrose, who was Trump's national security adviser for Gulf affairs until November 2018, said that while Pompeo and others may be touting the possibility of de-escalation, no one inside the White House believes that's the path Iran will choose.

She said there's likely a scramble inside the Pentagon, the State Department and the White House right now on multiple fronts.

First, the White House will be working on a package of intelligence it can share with U.S. allies to demonstrate what Pompeo called the "imminent threat" that Soleimani posed to American assets and personnel.

At the State Department, Pompeo has already been calling U.S. allies in the Middle East and Europe. Fontenrose said he's likely trying to gauge their willingness to help the U.S. with any possible retaliation from Iran and exchange intelligence about Iran's possible next move.

"These are going to be tough conversations," she noted.

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At the Pentagon, Defense officials will be reviewing and drafting contingency plans for possible Iranian attacks, with the hope of trying to "get in front of that and be ready for it."

Pompeo told CNN on Friday that the U.S. was already bracing for Iranian blowback.

"We’ve anticipated a wide range of possible responses and we have done our level best under the direct guidance of the president to prepare for all of those possibilities," Pompeo said.

Pompeo said Soleimani was "actively plotting in the region to take actions – a big action, as he described it – that would have put dozens, if not hundreds, of American lives at risk."

He declined to be more specific or disclose the intelligence information that suggested such an imminent attack. "The world’s a much safer place today," Pompeo said. "I can assure you that Americans in the region are much safer today after the demise of Qasem Soleimani."