The military and police, backed by Shia militias, Sunni tribal fighters and US-led coalition air strikes, are fighting to retake the city, 100 kilometers (60 miles) west of Baghdad, from the radical Sunni insurgents. But progress has been slow.
Deputy commander of Anbar Operations Command Major-General Abdel Rahman Abu Ragheef and Brigadier Safeen Abdel Majeed, head of the tenth division, were killed in the attack in the Jerayshi area along with three other people, said joint operations spokesman Brigadier General Yahya Rasool.
He told state TV the military had intercepted a explosives-laden vehicle targeting the forces, "but the resulting explosion led to (their) martyrdom". At least 10 others were wounded in the explosion, he said.
Separately, three people were killed in a suicide car bomb targeting a police checkpoint in the town of Bajwa, 15 kilometers (10 miles) northwest of Kirkuk.
There was no immediate claim of responsibility for either of the assaults.