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The Iraqi military warned the air strikes would have consequences while the foreign ministry said it summoned the U.S. and British ambassadors.
Iraq condemned overnight U.S. airstrikes on Friday, saying they killed six people and warning of dangerous consequences for a "violation of sovereignty" and targeted aggression against the nation's regular armed forces.
President Barham Salih said repeated such violations could cause Iraq to unravel into a failed state and revive the Islamic State militant group. Iraq's foreign ministry announced plans to bring a complaint to the United Nations.
The United States responded that all five targets were legitimate as they stored Iranian-supplied weapons used by the Kataib Hezbollah militia to attack the U.S.-led coalition.
"These locations that we struck are clear locations of terrorist bases," said Marine General Kenneth McKenzie, head of the U.S. military's Central Command.
Iraq's Joint Operations Command said in a statement that three soldiers, two policemen and one civilian were killed, according to an initial toll, and that four soldiers, two policemen, a civilian, and five militiamen were injured.
"The pretext that this attack came as a response to the aggression that targeted the Taji base is a false pretext; one that leads to escalation and does not provide a solution," Iraq's Joint Operations Command said in a statement.
The civilians killed and wounded were construction workers at an airport building site in the Shi'ite Muslim holy city of Kerbala, Iraqi religious authorities said.
McKenzie acknowledged that a structure had been hit near the Kerbala airfield but said it was being used to store weapons.
"That was a clear target," he said.
Around 5,000 U.S. troops remain in Iraq, most in an advisory capacity, as part of a broader international coalition formed to help Iraq drive back and defeat Islamic State militants.
But the Iraqi military said the new U.S. air attack went against "any partnership" under the coalition. "It will have consequences that subject everyone to the most serious dangers."
Iran's foreign ministry said on Friday that the "presence and behavior" of the U.S. and allied forces in Iraq was to blame for attacks against them.
The United States has conducted several strikes inside Iraq, killing top Iranian general Qassem Soleimani and Kataib Hezbollah founder Abu Mahdi al-Muhandis in January.
Many Iraqis say it is they who stand to suffer most from U.S.-Iranian tensions, and some, including caretaker Prime Minister Adel Abdul Mahdi, has called for U.S. troops to withdraw.
McKenzie said he was confident the United States would be able to keep troops in Iraq.
He added that while the latest U.S. strikes would deter militia from waging similarly deadly rocket attacks, the risk from Iran and the groups it backs remained high.
"I think the tensions have actually not gone down," he said.
Parliament passed a resolution calling for all foreign troops to leave after Soleimani was killed. The recent airstrikes could see those calls renewed.
Iraq has suffered decades of war, sanctions, and sectarian conflict, including the U.S.-led invasion of 2003.
Iraq is grappling with anti-government unrest in which almost 500 people have been killed since Oct. 1.
It also faces an unprecedented power vacuum after Abdul Mahdi stood down from most of his duties, and his designated successor withdrew his candidacy.