Police said on Sunday that assailants had opened fire on a cafe popular with Kurds in Kirkuk, 290km north of Baghdad, killing one and injuring three.
The cause of the attack in the ethnically mixed city was not known.
In the southern oil city of Basra, fighters hit a police patrol with a roadside bomb, injuring one nearby civilian.
Iraq's fighters appear to be scaling back attacks on US military forces while focusing its deadly efforts on interim government workers, primarily targeting the country's fledgling security forces.
A video posted on Sunday on the internet purportedly showed an interim Iraqi Interior Ministry official hostage being shot and killed by fighters from Abu Musab al-Zarqawi's network.
There was no way to independently authenticate the video.
The incidents took place while Christians gathered at the Virgin Mary church in Baghdad to celebrate Easter.
"We wish Iraqis in general and Christians in particular a happy Easter and wish them a happy year," said one parishioner, Sabah Rasam.
"We are brothers with all Iraqis and will remain so forever," said Rasam, part of a Christian community that accounts for an estimated 3% of Iraq's 25 million people.