About a dozen US troops were still there this week and spent Wednesday (August 31) supervising Iraqi army engineers repairing a 45 km (28 miles) bridge southeast to help local forces cross the Great Zab river in their push towards Mosul, the militants' de facto capital in Iraq which Baghdad wants to retake this year.
Loath to become mired in another conflict overseas, the White House has insisted there will be no American "boots on the ground" in Iraq, but current troop levels are approaching 5,000.
That is still a fraction of the 170,000 deployed at the height of the nine-year occupation that toppled Saddam Hussein in 2003, sparking an al Qaeda-backed insurgency and throwing the country into a sectarian civil war.
President Barack Obama withdrew US troops from Iraq but they returned in 2014 after the Iraqi army fled Islamic State's advance through a third of the country despite billions of dollars in US aid and training.
The United States is conducting an extensive air campaign over Iraq and also covert Special Forces raids against the jihadists behind their frontlines.
Washington says the focus of its troops in the country is to train, advise and equip local forces - Iraqi military and police, Kurdish Peshmerga and Sunni tribal militias, which are both battling Islamic State - and that US servicemen there have no combat role.
Advisers from the United States and other countries from an international coalition fighting Islamic State were initially confined to a few military bases across Iraq, but as the campaign progressed and Mosul comes into focus, Americans have inched closer to the action.
The US military, which tightly controls media access to its bases and no longer embeds reporters with troops like it did during the occupation, has tried to keep attention away from its activities in Iraq.
The soldiers who Reuters encountered on the bridge quickly turned their backs to cameras, and a Reuters request to visit Qayyara airbase, where the Pentagon is sending several hundred troops to help set up a logistics hub for the Mosul operation, was recently denied; Reuters reported.
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