Iraqi Prime Minister Haider al-Abadi ordered an urgent investigation on Friday into the fatal shooting of three Sunni clerics and the wounding of two others near the southern city of Basra.
The attack late on Thursday was carried out by four gunmen who opened fire from a speeding car on the clerics' vehicle, police sources said.
Previous attacks on Sunni and Shi'ite clerics have sometimes unleashed cycles of revenge killings in Iraq, where sectarian violence is at its worst since the height of the civil war some eight years ago.
A statement from the office of Abadi, the Shi'ite prime minister, said he ordered security commanders in Basra to "urgently work to reveal the circumstances of the attack" and arrest the perpetrators.
No one claimed responsibility for the latest attack.
Shi'ite militias have been accused of carrying out attacks on Basra's Sunni religious figures in the past. But two police officers said they suspected the involvement of Sunni militants from Islamic State, which the moderate clerics had urged local people to oppose.
"Initial investigation showed that one cleric's mobile was receiving death threat messages carrying the signature of Islamic State. We are still working to reveal the murderers and bring them to justice," said a police colonel, speaking on condition of anonymity.
Violence in Iraq killed at least 12,282 civilians in 2014, making it the deadliest year since the sectarian bloodshed of 2006-07, when the monthly death toll sometimes exceeded 3,000, according to the United Nations.