Katyusha rockets and indirect fire target US troops stationed in Iraq's Anbar province and in eastern Syria, officials say.
The remaining forces, some 2,500 US and 1,000 coalition troops, deployed in Iraq will remain in the country but will shift away from combat roles.
Two people wounded as 14 rockets targeted Ain al Asad air base in western Iraq, says a spokesperson for US-led coalition, which has been hit by a wave of attacks after America's air strikes on the Iraqi-Syrian border last month.
At least 10 rockets strike Ain al Asad air base in western Anbar province, officials say, two days before historic visit by Pope Francis to the country.
There are more than 5,000 American troops in Iraq now. Last month, the top US general for the Middle East said he believed the US will keep a smaller but enduring presence in the country.
To help Iraq in tackling Daesh, the US offered to move its troops to Iraq after the Syria pullout. But Washington faced an unprecedented denial from Baghdad.
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