The limited advances come as Iraq struggles to regain significant parts of the country after a lightning militant offensive led by the Islamic State (IS) jihadist group seized second city Mosul in June and swept through the country's Sunni heartland, as security forces fled.
The jihadist fighters have been bombarded since August 8 by US air strikes, allowing the peshmerga to claw back some lost territory, but the campaign has so far been limited to northern Iraq.
They also seized a main road used by the militants to transport fighters and supplies, and were close to sealing off all entrances to the town of Jalawla itself, which they have sought to recapture for weeks, the officer said.
"Jalawla is strategic because it is a gateway to Baghdad," Shirko Merwais, a senior Kurdish political party official in nearby Khanaqin, told AFP.
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Iraq "is carrying out air strikes and the peshmerga... are fighting on the ground," he said, adding that "in the beginning, coordination between the peshmerga and the Iraqi government was poor, but now, after the danger posed by (IS) grew, it has become much better."
In neighbouring Syria, where IS has also overrun large areas, the jihadists won a bloody battle for the Tabqa military airport, the last stronghold of the Damascus regime in the northern province of Raqa, a monitoring group and state media said.