"Our advance is slow because of the IEDs and booby-trapped roads," Brigadier-General Thamer Mohamed told the Reuters news agency.
"There is some resistance from the enemy, but it's mainly due to the booby-traps set up on the roads, in the houses, shops and government facilities. As you can see, our units are advancing and we have air support."
Several injured Shiite fighters said that the US was to blame for their injuries after striking their positions near Tikrit.
Since Thursday, when the US air strikes began, at least 17 Iraq security personnel have been killed and another 100 wounded around Tikrit, a security officer told Reuters.