Iraqi Prime Minister Nuri al-Maliki, facing Sunni extremists who have swept across his country from war-torn Syria, told the BBC that Assad's air force this week struck the insurgents on the Syrian side of the border, in a marked escalation.
State Department spokeswoman Marie Harf, while not confirming the air strikes, said that the United States believed military action by Assad would not be "in any way helpful to Iraq's security."
US President Barack Obama, who opposed the 2003 invasion of Iraq, has offered 300 military advisers to help push back the extremist forces but has opposed a wider involvement and blamed Maliki for alienating minorities.
Obama has also resisted calls for intervention in Syria against Assad, who has ruthlessly put down a rebellion waged by both hardline and moderate Sunni rebels.
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The chaos comes as the Obama administration explores repairing ties with Iran, a Shiite clerical state that has staunchly supported both Maliki, a fellow Shiite, and Assad, a secular leader from the heterodox Alawite sect.
Secretary of State John Kerry heads tomorrow for consultations with US ally Saudi Arabia, a conservative Sunni monarchy which is strongly critical of both Assad and Maliki.