They said the bomber drove his explosives-laden vehicle into the advancing troops north of Anbar's provincial capital, IS-held Ramadi, killing the two generals and three soldiers. A military spokesman said on state television that 10 other soldiers were wounded.
The officials spoke on condition of anonymity because they were not authorized to speak to the media.
A military statement read on state television identified the two generals as Maj Gen Abdul-Rahman Abu-Regheef, deputy chief of operations in Anbar, and Brig Gen Sefeen Abdul-Maguid, commander of the 10th Army Division.
Speaking on state television, military spokesman Brig. Gen. Yahya al-Zobeidi sought to play down the psychological effect of the loss of the two generals. "We will not stop our operations and we will continue to advance," he said.
There was no immediate comment on the attack from the Islamic State group.
The Islamic State group has controlled about a third of Iraq following a blitz across the north and west of the country in the summer of 2014. A US-led coalition has been staging airstrikes against IS positions in Iraq and Syria for about a year.
Government forces retook Beiji late last year from the IS, but the militants are on the offensive there again and now control about half of the town and the refinery, located to the north.
Iraq's prime minister, Haider al-Abadi, said this week that winning the ongoing battle over Beiji was key to defeating the IS in Iraq.
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