On Wednesday, three separate drone and rocket attacks targeted US diplomats in the nations. Fourteen rockets hit an Iraqi air base hosting US troops resulting in the injury of two American service members.
No group has immediately claimed responsibility for the attacks.
On Thursday, Pentagon spokesman John Kirby told reporters the attacks were “deeply concerning”.
“They are using lethal weaponry,” he said.
“I don’t know how you can say anything other than it is a serious threat.”
Analysts believe the attackers may have been part of a Iran-based militia groups.
Militia groups aligned with Iran pledged to retaliate against the US following American air strikes on the Iraqi-Syrian border last month which resulted in four deaths.
Iraqi military sources said the rocket attack on Ain al-Asad air base came from a rocket launcher fixed to a truck.
The device was concealed under sacks of flour.
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Early on Thursday, two rockets were fired at the US embassy inside Baghdad’s Green Zone.
However, the embassy’s anti-rocket defence system diverted one rocket away while the second fell outside the perimeter, security officials said.
In addition, a separate drone attack on the Al Omar oil field occurred late last month.
Following the drone attack, the Pentagon said a drone had been brought down in eastern Syria and that no US service personnel had been injured.
Iraqi army officials said the pace of recent attacks against US forces with rockets and drones is unprecedented.