The FAA said the ban was introduced due to the “hazardous situation” created by fighting between militants from the Islamic State (IS) and Iraqi security forces.
British Airways said it was suspending its flights over Iraq and would “keep the situation under review”.
The US launched air strikes against IS in Iraq on Thursday.
The FAA had previously banned all air travel over Iraq below 30,000 feet on 31 July.
On Saturday, Australian airline Qantas said it had suspended flights over Iraq, following similar actions by German airline Lufthansa, Dubai-based Emirates, Virgin Atlantic and Air France.
Flying over conflict areas has come under increasing scrutiny since the crash of MH 17 in Ukraine in July.
Earlier in July, the FAA and other European carriers briefly suspended flights to Israel’s Ben Gurion airport in Tel Aviv after a rocket landed near the airport.