The bombers attacked a regimental headquarters in the Haditha area of Anbar province late yesterday, killing Staff Brigadier General Ali Aboud, Lieutenant Colonel Farhan Ibrahim and four others, the sources said.
Major General Ali Ibrahim Daboun, the head of the Al-Jazeera Operations Command, said one suicide bomber blew himself up inside Aboud's office, while the other three detonated explosives elsewhere inside the headquarters.
Seven soldiers were also wounded in the attack, Daboun said.
IS overran swathes of Iraq, including large parts of Anbar, in a sweeping offensive launched in June 2014, but has largely been on the defensive in the province since the middle of last year.
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Iraqi tribesmen and security personnel defending Haditha, which lies near the country's second largest dam, have held off IS for more than 18 months with the help of air strikes by a US-led coalition.
The war with IS has taken a heavy toll on senior Iraqi officers in Anbar.
Senior army and police commanders have also been killed in other provinces.