Prime Minister Nuri al-Maliki, who was approved by parliament for a second term along with a national unity cabinet on December 21 after more than nine months of political deadlock, has cited security as one of his priorities.
Iraqi policeman and a Christian woman were killed on Monday in two different attacks in Baghdad, official said.
An Iraqi interior ministry official said that the gunmen killed Rafah Toma, as they broke into her home in central Baghdad and made off with a number of her possessions.
The official added that Toma lived alone in Al-Wahda neighborhood.
The latest incident comes as the Christians are being targeted in Iraq.
On Thursday, at least two Christians were killed and 16 others wounded in a wave of bomb attacks on Christian targets in Baghdad.
On October 31, militants stormed Our Lady of Salvation church in central Baghdad, leaving 44 people, two priests and seven security force personnel dead, in an attack claimed by Al-Qaeda's local affiliate, in Iraq.
Ten days after the church attack, a string of bomb and mortar attacks targeting the homes of Christians in Baghdad killed six people and wounded 33.
The interior ministry official, who would not be named, also said that a policeman was shot dead by gunmen with silenced weapons in Taifiya in northern Baghdad. He gave no further details.
The policeman's death followed a string of similar attacks on Sunday night in which a traffic police colonel, two other police, an army captain and an engineer were gunned down in five separate attacks in Baghdad by gunmen with silenced weapons.
A similar attack left a colonel with the interior ministry severely wounded.
Prime Minister Nuri al-Maliki, who was approved by parliament for a second term along with a national unity cabinet on December 21 after more than nine months of political deadlock, has cited security as one of his priorities.