A defence ministry official said they were heading to Najaf to bury a body.
The Iraqi capital has been racked by tit-for-tat attacks by members of the Shia and Sunni Arab communities in recent days.
Earlier, 10 Iraqi soldiers were killed in a raid in northern Iraq.
The army raided the village of Al-Salman, 260km northwest of Baghdad, but met resistance from armed villagers, a police source said.
In another incident, three people were killed and eight others wounded in a car bombing and a suicide bombing near Baghdad's heavily fortified Green Zone, police said.
The car bomb went off close to a restaurant about 100m from the Green Zone, the seat of the Iraqi government and headquarters of the US military.
A witness said a bomber blew himself up in front of the governmental compound in the Green Zone, killing five people and injuring ten others.
Iraqi police sources also confirmed that unidentified fighters abducted the Iraqi consul in Iran from his house in the al-Amel area of Baghdad.