The service member, whom the Pentagon confirmed was American, was at least the third killed by enemy fire in Iraq since IS overran swathes of the country in 2014.
President Barack Obama hailed the 2011 withdrawal of American troops from Iraq as a major accomplishment of his presidency, but US forces have been drawn back into combat in the country against IS.
"On May 3, 2016, a coalition service member was killed in northern Iraq as a result of enemy fire," the coalition said in a statement.
US Defence Secretary Ashton Carter said from Germany: "Our thoughts and prayers are with that service member's family."
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A coalition military official said on condition of anonymity that the service member was killed at 9:30 am (0630 GMT) by "direct fire" after "enemy forces penetrated" the Kurdish peshmerga forces' line.
Kurdish forces are deployed in Nineveh province, which is centred on Mosul, IS's main hub in the country.
IS attacked the peshmerga in multiple areas of northern Iraq on Tuesday in an attempt to "thwart the plan to liberate Mosul," said Jabbar Yawar, the secretary general of the autonomous Kurdish region's peshmerga ministry.
Tal Asquf is a small Christian town whose population fled when IS overran the region in the summer of 2014.
The United States announced last month that it was deploying additional forces to Iraq, bringing the official total to more than 4,000.
Pentagon spokesman Jeff Davis said the forces would be authorised to advise Iraqis at the battalion and brigade level as opposed to larger divisions, potentially exposing them to greater risks closer to the front lines.