Sabah Al-Karhout, president of the Anbar Provincial Council, told The Associated Press the ambushes took place Friday west of the provincial capital, Ramadi, but said he had no more details. There was no immediate word from federal authorities or the Islamic State group.
The Islamic State group controls much of the vast Anbar province, including Ramadi and the city of Fallujah. Government forces and Shiite militiamen have been trying to dislodge Islamic State fighters from the province but they have been making slow progress.
Later, a statement posted on the ministry's official website said al-Obeidi on Saturday also fired the commander of a brigade deployed in Anbar as part of the 10th Mechanized Infantry Division. It did not name the commander, but added that he failed to carry out his duties.
"There is no place for those who neglect to carry out their missions and duties. Those who want victory must be on the front line," it quoted the minister as saying.
The Islamic State group controls about a third of Iraq and neighboring Syria and has established a self-declared "caliphate" across its territory.