Defense Department spokesman Jonathan Hoffman said: “It is clear that these missiles were launched from Iran.”
Military bases at Ain Al-Assad and Irbil were hit, he said, adding that “initial battle damage assessments” were being conducted.
Iran’s Islamic Revolutionary Guards Corps (IRGC) claimed responsibility for the attacks, Iranian state television and state news agencies reported.
The attack on the Ain Al-Assad base, which hosts U.S. troops, was “a total success by all accounts,” the IRGC said.
The IRGC stated the multiple attacks were in retaliation for the killing of a prominent Iranian military commander, Qasem Soleimani, who died in a U.S. airstrike last week.
A communique from the Iranian military promised “more crushing responses” should the United States respond to the attacks.
It further added that the operation is code-named “Martyr Soleimani” and advised the United States to withdraw its troops from the region to prevent the killing of soldiers.
It was unclear what other sites may have been attacked.
“We are aware of the reports of attacks on U.S. facilities in Iraq,” the White House told reporters based on a media pool report. “The President [Donald Trump] has been briefed and is monitoring the situation closely and consulting with his national-security team.”
The multiple attacks came hours after Soleimani was buried in his hometown on January 7.
Iran’s military leaders and pro-Iranian factions in Iraq had vowed to avenge his death.
A day earlier in Washington, U.S. Defense Secretary Mark Esper told reporters that he anticipated Iran would retaliate for the death of Soleimani “in some way, shape, or form.”
“We’re prepared for any contingency. And then we will respond appropriately to whatever they do,” he warned.