The forces start their day with dawn prayers. Then, if there are Islamic State fighters on the road ahead, artillery opens up to drive them back, targeting in particular suspected suicide car bombers. Armored vehicles advance to clear snipers, trying to avoid bombs planted by retreating militants.
The militiamen and soldiers say they have information about the territory ahead from military intelligence and sources in Islamic State territory. Sometimes that takes them on detours to bypass suspected booby-traps on their way.
Even so, the first two days of operation brought losses. Three blackened, bombed-out vehicles belonging to the army and militia forces could be seen on the road.
On Monday, crossing the hilly Hamrin region before descending into the flat Tigris plain, the fighters advanced only 8 km (5 miles). The next day, as Islamic State fighters evaporated, their progress was closer to 50 km.
As they advanced, they left police units and militia fighters to hold territory behind the frontline.
By mid-afternoon on both days, they set up base for the night. A bullet-pocked excavator, with metal armour-plating to protect the driver, dug a defensive wall for their base.
Driving alongside them in a white pick-up truck with loudspeakers and a Shi'ite banner on its roof, men from the Ideological Guidance unit dispense battlefield advice and blast out military songs to raise the fighters' spirits.
"Mosul is calling you," one of the songs - a favorite among the Badr Organisation - rings out, referring to the northern city which is the ultimate goal in Baghdad's military campaign to eliminate Islamic State.
The eastern force, which is targeting the town of al-Alam north of Tikrit, is one of three main axes of the campaign, the other two advancing along the Tigris river from north and south.
The militia fighters have already contacted the mainly Sunni al-Alam residents to say they will be well-treated if they put up white flags. But the campaign is clearly presented to the Shi'ite fighters as a defense of their sect, from Sunni radicals who consider Shi'ites heretics.
"Without you, the women of Karbala and Najaf will be enslaved," Rubaei told the fighters assembled in Udhaim before the fight, referring to holy cities that house the two most important Shi'ite shrines.
"Today, thanks to you, we are all victorious. Today we are in their hotbeds."