The Pentagon's mission against the Islamic State in Syria remains open-ended despite President Donald Trump's promise of a quick U.S. withdrawal.

Military leaders are focusing on pushing the once-powerful group out of the small foothold it controls in eastern Syria and ensuring that it cannot plot attacks against the United States, a task defense officials have suggested will require a U.S. footprint after the fighting stops.

What remains unclear is how the military will reconcile its vision with that of the president, whose distrust of foreign wars and desire to demonstrate a swift victory were evident in the past week as he vowed that U.S. troops would depart Syria "very soon."

"I want to get out. I want to bring our troops back home," Trump said. "It's time."

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Public and private comments reveal a gap regarding America's future role in Syria. Military leaders, mindful of the fleeting nature of earlier military gains in Iraq and Afghanistan, have spoken repeatedly of the need for a robust post-conflict agenda.

Gen. Joseph Votel, the head of U.S. Central Command, predicted that the "hard part" lies ahead, as Syrian towns and cities now free of the Islamic State seek to rebuild and ensure that militants cannot return.

"Of course there is a military role in this," he said.

While commanders warn against leaving before the territory is stable enough to prevent an insurgent revival, the president wants other countries to stabilize the area.

Meeting with senior national security aides the same day, the president sought to limit U.S. involvement in stabilization activities, but did not press for an immediate withdrawal.

Military officials are trying to address Trump's concerns even as they race ahead with their plans for what many have described as "finishing the job."

"The president has actually been very good in not giving us a specific timeline, so that's a tool that we can use to our effect as we move forward," Lt. Gen. Kenneth McKenzie, director of the Joint Staff, told reporters this week.

In an indication of an evolving Pentagon approach, Defense Secretary Jim Mattis suggested Friday that the United States had not decided whether it would continue supporting its main partner in northern Syria after withdrawing troops. "We'll work all this out," he said.

For now, military leaders are centering their efforts on the remaining military mission, which presents a sharp contrast to the one they faced in 2014, when militants controlled a vast swath across central and eastern Syria.

After more than four years of intensive airstrikes and U.S.-supported ground operations, only a tiny fraction of that militant domain remains. Estimates of how many Islamic State fighters are currently in Syria and Iraq range from roughly 1,000 to 3,000, but the message from U.S. commanders is clear: A tactical victory is within reach.

Today, about 2,000 U.S. troops arrayed across northern and eastern Syria conduct a variety of missions. Chief among those is dealing with a small militant force dug in along the Euphrates River near the city of Bukamal, on Syria's border with Iraq.

There, U.S. forces advise and support members of the Syrian Democratic Forces (SDF), a Kurdish-dominated force that has been the main American military partner against the Islamic State.

After years of steady progress reclaiming militant-held territory, military leaders expressed frustration when the SDF diverted its efforts to defending the northwest city of Afrin from an onslaught by Turkish-backed Syrian forces.

Turkey has supported an aggressive campaign seeking to ensure that Syrian Kurds, whom it considers terrorists, cannot consolidate positions along its border.

While some Islamic State fighters remain, the campaign against them ground to a near-halt after key SDF leaders departed for Afrin. "The military was within weeks of accomplishing the military component of ISIS fight," said Jennifer Cafarella, who tracks events in Syria at the Institute for the Study of War.

In northern Syria, U.S. troops are expanding their activities around the city of Manbij, where the same Kurdish-Turkish tensions have the potential to erupt in greater violence and, U.S. officials fear, to allow the Islamic State to return.

In the city of Raqqa, which was the seat of Islamic State power until last year, a small number of U.S. troops supports contractors ridding the city of improvised bombs and a civilian mission working to restore governance and basic services.

As they are in other areas across northern and eastern Syria, U.S. troops are also training a new local force to keep Raqqa secure.

U.S. troops are also supporting internal security forces in areas along Syria's porous borders. Militants control another pocket of territory in the Euphrates River valley southeast of Deir al-Zour approaching the Iraqi border.

Late last month, Marine Corps Col. Seth Folsom described the Islamic State groups remaining in Syria as "small, disorganized, fractured groups of ISIS fighters" that local forces are seeking to hunt down one by one.

Even if the Islamic State loses every inch of territory it still holds, American military commanders warn that the extremist group will transform into an insurgency.

In a recent report for the New America think tank, analysts David Sterman and Nate Rosenblatt warned that while the U.S. military has rolled back the Islamic State's physical caliphate, it has not addressed the root causes that gave rise to the mobilization of its fighters in the first place. They said that economic growth and political inclusion in the areas where the Islamic State recruited insurgents were critical to stopping a similar group from emerging.

The discussions about the future of Islamic State operations are just the latest attempt to craft a successful approach to a conflict whose complexity has defied U.S. policymakers since it erupted in 2011. They take place as the larger Syrian war continues, with a strengthened Syrian government extending its control over rebel areas thanks to support from Russia and Iran.

Anthony Cordesman, a former Pentagon official now at the Center for Strategic and International Studies, said Russia was unlikely to act as a stabilizing force that would work with the Assad regime to prevent the Islamic State from re-emerging.

"Russia is doing a superb job of playing a spoiler role," Cordesman said. "But it is neither capable of dominating a country on the ground nor is it capable of funding any serious form of rebuilding and development."

Cordesman warned that a precipitous exit from Syria could allow militants to regroup and launch attacks into western Iraq.

Although Trump has repeatedly emphasized the need to withdraw U.S. troops from Syria, he has said very little about his perspective on the U.S. military footprint in neighboring Iraq.

About 5,000 American troops have been helping local forces eradicate the Islamic State and stabilize recaptured territory.

Authors information: The Washington Post's Karen DeYoung, Shane Harris, John Hudson and Carol Morello contributed to this report.