BAGHDAD—Syrian warplanes carried out airstrikes in western Iraq, stepping up the military role of the U.S. adversary in helping Baghdad's Shiite-dominated government fight Sunni insurgents.

The strikes on Tuesday came as the Pentagon announced that the first 130 members of a potential 300 U.S. military advisers were in place in Baghdad to start assessing and improving the Iraqi army's ability to counter the gains of rebels led by the Islamic State of Iraq and al-Sham.

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