President Trump's inclusion of Iraq in his executive order limiting travel to the U.S. from seven Muslim-majority countries is putting a strain on U.S.-Iraqi relations, potentially hindering the fight against the Islamic State in Iraq and Syria (ISIS).

Iraqi Prime Minister Haider al-Abadi now has a choice: He can either enforce a reciprocal ban on U.S. visas, which could drive American military contractors out of the country, or accept the policy, which could leave an opening for a leader less supportive of America to take his place.

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"I think the Iraqis were extraordinarily offended, not unnaturally," said Danielle Pletka, a senior vice president for foreign and defense policy studies at the conservative American Enterprise Institute. "It's true that one of the I's in ISIS does stand for Iraq, but we're fighting ISIS with the Iraqi military."

Trump’s order prohibits citizens from seven predominantly Muslim nations from entering the United States for at least 90 days while vetting procedures are reviewed. The order also halts the acceptance of refugees for 120 and indefinitely pauses the Syrian refugee program. In addition to the Iraq, those countries are Syria, Iran, Sudan, Somalia, Yemen and Libya.

Of the seven countries, Iraq is the only one where the United States has a full diplomatic presence.

The Trump administration has defended the order as necessary to protect the United States from would-be terrorists.

“The president's going to be very proactive with protecting this country,” White House press secretary Sean Spicer said Monday. “We're not going to wait until we get attacked and figure out how we can make sure it doesn't happen again.”

But the policy is creating a headache for the Pentagon as it seeks to drive ISIS out of Iraq.

About 5,000 U.S. troops are in Iraq, with hundreds embedded on the ground with Iraqi forces in and around Mosul.

The U.S. military has also relied on thousands of contractors to support its efforts, taking on roles including logistics and maintenance, construction, security, translation, and transportation. There are also thousands of additional contractors in Iraq helping the State Department.

The U.S. coalition is now participating in a high-stakes fight to retake Mosul, Iraq’s second-largest city. Iraqi forces have recaptured the part of the city east of the Tigris River, but the western half has proved tougher to penetrate.

With the battle to retake Mosul from ISIS raging, the Pentagon can ill afford a diplomatic dispute with the Iraqi government.

On Monday, the Iraqi parliament approved a measure to ban Americans wishing to travel to Iraq in response to Trump’s ban of Iraqis. Should Trump not rescind his ban, the measure says, Iraq should reciprocate “to maintain the state prestige and the dignity of the Iraqi people.”

The measure does not specify to whom the ban would apply, but U.S. experts said that, if enforced, it would likely affect contractors the most.

But the Iraqi parliament cannot enforce the measure. That power falls to Abadi.

Robert Ford, deputy U.S. ambassador to Iraq from 2008 to 2010, said he does not foresee Abadi enforcing the ban, beyond perhaps blocking several people from entering the country to make a point.

“To the extent that American contractors are helping with the logistics of the American military, I don’t think Abadi would want to severely impede that,” Ford said.

Indeed, Abadi said Tuesday he wouldn’t act on parliament’s vote.

“We will not do anything of the sort,” he said at his weekly news conference, according to a translation from Reuters. “We are studying [possible] decisions, but we are in a battle, and we don't want to harm the national interest.”

But such a decision by Abadi could have long-term repercussions, Ford added. Specifically, it could give rival and former Prime Minister Nouri al-Maliki fodder to accuse Abadi of caving to the United States.

Maliki has been blamed for sectarianism that fostered ISIS’s growth and is seen as more pro-Iran than Abadi.

“This executive order from Trump embarrasses Abadi,” Ford said. “It makes him look weak. Maliki benefits politically from this at the expense of Abadi, and putting Maliki back in the prime minister’s office would not be a good thing.”

In an op-ed for The Washington Post, retired Marine Gen. John Allen, who served as special presidential envoy for The Global Coalition to Counter ISIL from 2014 to 2015, and Michael O’Hanlon, a senior fellow at the Brookings Institution, also argued that Trump’s order undercuts Abadi’s power, hurting the ISIS fight.

“At the very moment that Trump has sought to up the game against the Islamic State, his words and actions treat Iraq and Iraqis as though they’re irrelevant to the defeat of this organization,” Allen and O’Hanlon wrote. “Indeed, the worst blows potentially preventing the defeat of the Islamic State have been landed by Trump himself and could lead to the end of the U.S. mission and American influence there.”

Even if parliament’s ban goes nowhere, it symbolically shows Iraqi public opinion turning against America, said Stephen Biddle, an adjunct senior fellow for defense policy at the Council on Foreign Relation.

“It boxes Abadi in and reduces his flexibility to respond to American policy preferences,” Biddle said.

Biddle also highlighted the issue of Iraqi F-16 pilots who are now training in Arizona. Even if those pilots are ultimately granted an exemption to come to the United States, as the Air Force is expected to request, the disruption in training can only hurt the Iraqi military’s effectiveness, he said.

But the “gravest damage” to the fight against ISIS, Biddle said, is playing into its narrative that the West is at war with Islam.

“All the painstaking efforts by the two previous presidents” to avoid that, Biddle said, “just got thrown in the trash can.”