In al-Madan, south of Baghdad, an Iraqi police patrol came under fire, killing one policeman early on Saturday.
In the western Baghdad neighbourhood of Yarmuk, three mortar rounds exploded, injuring another officer near a local police station.
In the northern district of al-Adhamiya, six rounds rained down, with one landing in a schoolyard and slightly damaging the building, which was unoccupied.
After several days of relative calm during Iraq's constitutional referendum, attacks have resumed in the past few days, including the killing of a defence lawyer for one of Saddam Hussein's co-defendants and the brief kidnapping of an Irish reporter.
Three US soldiers were killed in Iraq while conducting combat operations when their vehicle came under fire with an improvised explosive device in the vicinity of al-Nassir Wa al-Salaam on 20 October, a US military statement said.
During the subsequent engagement, US forces said they killed two fighters and detained four others suspected of involvement in the attack.