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

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

Obeidi said the death toll was a "correction" to earlier statements that said just one Iraqi soldier had died, a fact that was disputed by soldiers who witnessed the strike.

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

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

Carter said the details of how the incident took place were not yet clear. U.S. officials are now investigating. They declined to give details of how each side may have played a role.

Carter 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.

Carter, when asked whether the incident could increase political pressure on Abadi, said that he hoped "Iraqis will understand that this is a reflection of things that happen in combat."

In a statement on Saturday, Abadi's office said the prime minister had called for "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.