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There have been no flights between the neighboring countries since former Iraqi President Saddam Hussein invaded Kuwait in 1990.
Saudi Arabia and the United Arab Emirates are both wooing Baghdad now in an effort to halt the growing regional influence of arch-foe Iran.
"Baghdad International Airport today welcomed the first Saudi plane after a 27-year break," said a ministry statement cited by local media. "This plane belongs to the Saudi company Flynas."
Flynas, which launched as Nas Air in 2007 and first turned a profit in 2015, is facing increasing competition in Saudi Arabia, its primary market. It said last week it would soon start flights to several Iraqi cities.
In August the two countries said they planned to open the Arar land border crossing for trade for the first time since 1990.