BEIRUT — U.S.-backed forces have launched what they hope will be the final battle for territory in the four-year old war against the Islamic State 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.-backed Syrian Democratic Forces began the offensive Monday night, advancing toward the town of Hajin on the eastern bank of the Euphrates River aided by U.S. airstrikes, U.S. and SDF 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 the Islamic State’s 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 area 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 Islamic State 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 entire war, with experience gained in battles such as Mosul and Raqqa.