"We lost 10 of our soldiers," Khaled al-Obeidi said in Baghdad, adding that "an investigation into the incident was opened."
A statement from the Joint Operations Command yesterday mentioned that 10 had been "wounded or killed" but Obeidi and another senior military source clarified today that 10 troops were killed.
According to the joint command, the incident occurred when two coalition strikes allowed Iraqi ground forces to advance rapidly towards positions held by fighters of the Islamic State group south of their stronghold of Fallujah.
The US military acknowledged a coalition strike may have caused casualties among the ranks of the Iraqi security forces it supports in Fallujah and elsewhere in the country.
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"Despite coordination with the Iraqi security forces on the ground, initial reports indicate the possibility one of the strikes resulted in the death of Iraqi soldiers," a statement said yesterday.
It said the US military would launch its own investigation into what it described as likely the first "friendly fire" incident involving the coalition since the war against IS was launched last year.
US Defence Secretary Ashton Carter, who was in Iraq the day before the incident, called Prime Minister Haider al-Abadi to extend his condolences, a statement said.