– U.S.-backed forces have launched what they hope will be the final battle for territory in the four-year-old war against ISIS with an assault on the militants' last major holdout in the eastern Syrian desert, the U.S. military said Tuesday.

Ground forces with the U.S. and Kurd-backed Syrian Democratic Forces (SDF) began the offensive Monday night, advancing toward the town of Hajin on the eastern bank of the Euphrates River aided by U.S. airstrikes, officials said.

Hajin is the largest town in an approximately 95-square-mile stretch of mostly desert terrain along the river's east bank. The conquest of this territory would mark an effective end to ISIS' so-called caliphate, which at its peak in 2014-2015 spanned vast areas of Syria and Iraq.

The battle, however, won't spell an end to the threat posed by the militants, who are already regrouping in pockets of territory in Iraq and also maintain cells scattered across the vast desert to the west of the Euphrates, which is under Syrian government control.

U.S. military officials say they are anticipating a tough fight for the Hajin area, which has served as the final retreat for ISIS fighters who chose not to surrender or flee earlier battles. U.S. and SDF estimates put their number at between 1,500 and 2,500, out of an army that may have numbered as much as 100,000 at the height of the group's prowess.

But they include the toughest and most ideologically committed militants of the war, with experience gained in the Mosul and Raqqa battles. They are unlikely to give up easily, said Col. Sean Ryan, a U.S. military spokesman in Baghdad. The militants have laced the area with underground tunnels, riddled it with explosive devices and are expected to launch suicide attacks rather than submit.

Ryan would not put a timeline on the fight but said it is not expected to continue past the end of the year. Kino Gabriel, a spokesman for the SDF forces, which will bear the brunt of the ground fighting, said many foreign fighters are among those making a last stand in the Hajin pocket.

It has also been widely speculated that the town, or one of the surrounding villages, could be the hiding place of top ISIS officials, including perhaps their leader, Abu Bakr al-Baghdadi. Secretary of Defense Jim Mattis said Tuesday that he "wouldn't be surprised" if some ISIS leaders were in the Hajin area.

But, Gabriel said, it is more likely that Baghdadi has already escaped the U.S.-led coalition's dragnet and is taking refuge in one of the other pockets loosely controlled by ISIS. "There is a possibility that Baghdadi is in that area, but there are a lot of areas in both Syria and Iraq that he could be hidden in. I don't think he would allow himself to be surrounded from all sides," he said.

The offensive in eastern Syria comes at a time when international attention has been focused elsewhere in the country — on Idlib Province in the northwest, where Syrian government forces are massing for a possible assault on a rebel stronghold.

The offensive for Hajin, code name Operation Roundup, has been months in the making. It comes after Trump administration officials put an end to the uncertainty surrounding the fate of the northeastern Syrian enclave controlled by the SDF by declaring that U.S. troops would stay indefinitely.

The U.S. maintains about 2,000 troops in northeastern Syria, across an area amounting to more than a quarter of the country. They were dispatched to aid in the fight against ISIS, and in the process they helped expand the Kurdish-dominated SDF into vast areas of mostly Arab-populated territory.

A withdrawal would have left the area vulnerable to the ambitions of the Syrian government to reclaim all of the territory it lost after the uprising against President Bashar Assad in 2011.

But earlier this month, Trump administration officials said that U.S. troops will remain indefinitely, pending an overall solution to the Syrian war, both to ensure that ISIS doesn't return and Iran doesn't expand its influence.