Raikan Mahdi, the head of the security committee for Al-Zubair district in Basra province, said "unknown gunmen" killed the clerics and wounded two more.
Mahdi said the attack took place as the clerics headed from provincial capital Basra to Al-Zubair on Thursday night, after attending a meeting on preparations to celebrate the Prophet Mohammed's birthday.
It is still unclear who carried out the killings, which come at a time of heightened tensions between Iraq's Shiite Muslim majority and the Sunni Muslim minority who mark the prophet's birthday on Saturday.
Sunni jihadists from the Islamic State (IS) group spearheaded a sweeping offensive that overran major parts of Iraq and have repeatedly attacked Shiites, whom the consider to be apostates.
Baghdad turned to Shiite militias for support against IS, and while they have played a key role in the fighting, they have also carried out kidnappings and extrajudicial killings targeting Sunnis.
Prime Minister Haider al-Abadi, a Shiite, condemned the Basra killings, saying they were carried out by "terrorist gangs" who must be brought to justice.
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Interior Minister Mohammed Ghabban -- a member of the Badr bloc, which is affiliated with one of the country's most powerful Shiite militias -- ordered an investigation into the attack, the ministry said, blaming it on "forces serving the (IS) project."
But Basra is far from IS strongholds, which are located north and west of Baghdad, and parliament speaker Salim al-Juburi, a Sunni, implied that Shiite militiamen were behind the attack.
"We will not allow the replacement of the civil state that we seek to build with a group of warlords and militia leaders," Juburi said in remarks on the killings, according to a statement released by his office.
And the Iraqi Islamic Party, a main Sunni political party of which Juburi is a member, also said the attack was carried out by "criminal militias."
Baghdad's reliance on Shiite militias has helped push back IS but also increased their power to the point that controlling them will be a major challenge for the government.
But the Iraqi government's first priority is the fight against IS, and while pro-government forces have regained some ground, large areas are still outside Baghdad's control.