The deaths occurred when three ISIS attackers targeted a forward combat outpost in al-Mazra, between Karma and Falluja, said an Iraqi police officer and a security source near the scene.
The Iraqi military operation against ISIS was announced Tuesday, a little more than a week after the militant group overran Anbar's provincial capital, Ramadi
Iraqi soldiers and security forces are fighting alongside a key Shia militia group, Hashd al-Shaabi, as they seek to push back the Sunni extremist militants.
Officials: University retaken
There was better news for Iraqi forces elsewhere in Anbar, however.
Iraqi soldiers battled alongside fighters from the Iraqi branch of Hezbollah's Shiite militias -- part of Hashd al-Shaabi -- to retake control of the University of Anbar on the southernmost edge of Ramadi from ISIS militants, two Sunni sheikhs in Anbar province told CNN.
Iraq's state television channel, Iraqiya TV, also reported Wednesday that the Iraqi military and members of the Hashd al-Shaabi militia had managed to defeat ISIS militants in al-Ankur, a few kilometers south of Ramadi, and had entered the university.
Col. Steven Warren, spokesman for the U.S. Defense Department, said Wednesday that the United States has seen no indication that any force other than ISIS was inside Ramadi.
ISIS continued to fortify berms and lay booby traps and roadside bombs, Warren said. The militants were able to bring supplies into Ramadi through some routes from the west, with Iraqi forces remaining largely east and south of the city, according to Warren.
Last week, the Iraqi government said its air force had bombed the university and killed dozens of ISIS militants. ISIS has controlled the Ramadi neighborhood of Tamim, just north of the university, for months.
Meanwhile, more than 200 ISIS militants have been taken captive by Hashd al-Shaabi in Anbar province, according to the militia's security spokesman, Youssef al-Kelabi. Al-Mayadeen TV aired pictures of the alleged militants on Wednesday.
Local tribesman and tribal leaders who spoke to CNN disputed the number of militants captured, however, saying there were only 20 to 25 ISIS members in the area. The other men shown on TV were fishermen and farmers, they said.
Will to fight?
ISIS fighters swept into Ramadi on May 17, tightening control of Anbar province and gaining a base of operations about 110 kilometers (70 miles) away from Baghdad.
U.S. Defense Secretary Ashton Carter publicly criticized the Iraqi army
over the weekend, saying it lacked the will to fight. The Obama administration has since sought to mend fences
White House communications director Jen Psaki told CNN's "New Day"
that what Carter had said is "what he was seeing and hearing from the ground, but also the Iraqis themselves have acknowledged that there were some command issues, some issues on the ground and it's something they want to adapt to as well."
Progress has been made by the Iraqis, she said, but it takes time for efforts to strengthen the armed forces, tackle division, arm them and train them to take effect.
"It's important for people to remember the Iraqi security forces have also retaken 25% of populated areas from ISIL," she said, using an alternative acronym for ISIS. "There are going to be ups and downs here.
"We need to continue to adapt and we need to continue to prepare them and equip them with what they need, as does the international coalition."