Defense Secretary Ash Carter talks to troops at the Baghdad International Airport, July 23.

BAGHDAD — Kurdish Peshmerga forces retook a swath of northern Iraq late last month from ISIS and days later American forces appeared in the area, the latest sign of increasing U.S. military activity in the country.

The U.S. troops, numbering about a dozen, were still there this week and spent Wednesday supervising Iraqi army engineers repairing a bridge 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 Obama withdrew U.S. troops from Iraq but they returned in 2014 after the Iraqi army fled ISIS’s advance through a third of the country despite billions of dollars in U.S. aid and training.

The United States is conducting an extensive air campaign over Iraq and also covert special forces raids against the terrorists behind their frontlines.

But Washington says the focus of its troops in the country is to train, advise and equip local forces.

While the U.S. military advisers and the soldiers who protect them do not have a combat mission, circumstances have at least occasionally blurred their role and brought them into contact with ISIS. At least three American service members have been killed by the terrorist group.