An airstrike by the U.S.-led coalition this past week killed 10 Iraqi troops, the Iraqi government said Saturday, in an apparent friendly fire incident in which the U.S. defense secretary says both sides shared responsibility.

Iraqi Defense Minister Khaled al-Obeidi, at a news conference in Baghdad, said one Iraqi officer and nine soldiers were killed in the strike Friday, which took place south of the city of Fallujah, about 40 miles west of Baghdad.

Obeidi said the death toll announcement was a “correction” to earlier statements that one Iraqi soldier had died — statements that were disputed by soldiers who witnessed the strike.

U.S. Defense Secretary Ashton B. Carter said an American aircraft appeared to have conducted the strike, which he called “a mistake that involved both sides.”

Carter called Iraqi Prime Minister Haider al-Abadi on Saturday to express his condolences for the deaths.

Speaking during a visit Saturday to the USS Kearsarge, an amphibious assault ship stationed in the Persian Gulf, Carter said the details of how the incident took place were not yet clear. U.S. officials are investigating; they declined to give details of how each side may have played a role.

In the call Carter placed from the Kearsarge, he said that both he and Abadi voiced regret for Friday’s loss of life. “It’s tragic,” Carter told reporters. “But he and I both recognized that things like this can happen in war.”

According to the U.S.-led coalition, the strike was one of two that took place around Fallujah. The strikes hit an Islamic State tactical unit, militant vehicles and fighting positions, and a construction vehicle.

The incident, which comes as Abadi’s government weighs embracing further support from the United States, is likely to be used for political gain by critics of U.S. military assistance in Iraq, including the country’s Iranian-backed Shiite militias.

Earlier in the week, Carter and Abadi held talks in Baghdad in which the prime minister, wary of being seen as too reliant on U.S. assistance, did not accept an offer of accelerated support for Iraq’s ongoing campaign to retake the city of Ramadi.

Ramadi is a key test for Abadi, who has focused on recapturing cities under militant control since taking power in 2014.

Smoke from a U.S.-led coalition airstrike billows above Sinjar as part of a major offensive launched today to expel Islamic State militants from the Iraqi city. (Alice Martins/The Washington Post)

Carter, when asked whether the incident could increase political pressure on Abadi, said he hoped that “Iraqis will understand that this is a reflection of things that happen in combat . . . but it’s also a reflection of how closely we are working.”

Carter said he and Abadi agreed to continue their joint fight against the Islamic State. The Obama administration in recent weeks has rolled out new military measures designed to be more effective against the group, which is firmly entrenched in much of Iraq and Syria despite more than a year of U.S. and allied airstrikes.

The Pentagon has proposed employing U.S. combat advisers and Apache attack helicopters for the offensive in Ramadi and a future one to the north in Mosul, but Iraqi officials have not accepted that offer. President Obama has said that U.S. troops can advise and support Iraqi forces but that they cannot take part in combat in earnest.

Abadi’s office said Saturday that the prime minister, while speaking with Carter, had called for the “most accurate measures to be taken to avoid such painful incidents” as the friendly fire deaths. He said his government was working with the United States to investigate what Abadi called an “error.”

“It must not be repeated,” Abadi said.

Obeidi, the defense minister, said in an interview with The Washington Post that “the guilty” would be punished according to Iraqi laws.

“We will never relent on Iraqi blood. . . . Whoever was guilty, it will not go without punishment,” Obeidi said.

The U.S. military normally does not allow its troops to be subject to local courts for actions that take place in the course of their military activities.

Unlike Abadi, Obeidi refused to describe the alleged coalition airstrike as accidental, saying that such conclusions must await the results of the investigation. According to U.S. officials, the U.S.-led coalition has invited the Iraqi government to take part in that probe.

The incident also highlights the risks that U.S. forces face in their renewed combat role in Iraq, not just from the Islamic State.

Abu Alaa al-Walaie, who heads Kitaeb Sayyid al-Shuhada, a Shiite militia, said in a statement that “Americans are killing our soldiers and then express their con­dolences for killing them.”

“The resistance will respond with the same act for revenge,” the statement said.

U.S. forces battled Shiite militias for much of the war that followed the 2003 invasion to oust Saddam Hussein.

According to the Iraqi military, Iraqi forces requested air assistance Friday near the town of Amiriyat al-Fallujah because poor weather prevented Iraqi planes from conducting that support on their own. When the strike occurred, Iraqi forces and militants were situated close together. “Our forces got mixed,” the military said.

The Iraqi military said a third strike had taken place.

A U.S. defense official said the plane that conducted the strike was a B-1 bomber.

Speaking aboard the Kearsarge, a senior U.S. defense official said that poor weather appeared to have been a factor in the incident, as did the fact that Iraqi forces were closer to the target area than U.S. forces had understood at the time.

The United States remains “fully committed to the security and the safety” of Iraqi forces, said the official, who spoke on the condition of anonymity.

Abadi had been “very understanding that these things happen when you’re trying to really increase the pace of operations,” the official said. He “did not have hard feelings about the incident.”

Loveday Morris contributed to this report.

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