Informed sources told Aljazeera that al-Maliki said the breakaway province would include Basra, Misan and Dhi Qar governorates.
He also wants to shut Basra's port and in effect stop oil exports.
Al-Maliki said the decision was taken because the Iraqi interim government was "responsible for the Najaf clashes".
He has not outlined the steps for the implementation of his proposal.
Ali Hamud al-Musawi, head of the Misan governorate council, told Aljazeera al-Malki's decision was a normal and a logical reaction.
"The feelings of Iraqi southerners in particular and Iraqis in general had been contempt," al-Musawi said.
"This reaction comes in response to the crimes committed against Iraqis by an illegal and unelected government, and occupation forces who claimed they came to liberate Iraq, but it turned out that they have come to kill Iraqis," he added.
Al-Musawi expressed support for what he described as "our brothers in Basra" and announced that negotiations were going on regarding the activation of the breakup.
"Nothing would shock me, we heard of the break-up scenario a long time ago, and it seems that the atmosphere in Iraq nowadays is suitable to carry out any pending agendas"
Dr Dhafir al-Ani,
Iraqi political analyst
"We are discussing the decision and we will stop Misan's oil flow, until Baghdad's government restores its logic and realises that millions of Iraqis care for the people of Najaf and Karbala," he said.
"Iyad Allawi should not expect us to support him," he said. "We expected this government to give us justice, democracy and freedom," he added.
Al-Musawi said the interim government did not open communication channels with Iraqis and used force against them instead.
"We support the unity of Iraq when there is an Iraqi government that acknowledges all people's rights," al-Musawi said.
"The government should not make irresponsible decisions and attack our religion," he added.
State minister of the Iraqi interim government, Adnan al-Janabi, has played down the breakup call.
"The deputy of Basra governor is merely an Iraqi official in the municipal council of Basra, and does not represent the government," he said.
Al-Janabi denied any negotiations
with al-Sadr were underway
"We do not recognise him, let him say whatever he likes."
He denied reports that suggested negotiations with Shia Muslim leader Muqtada al-Sadr were underway.
"They [al-Sadr militias] are outlawed, they must go out of Najaf," he said.
The state minister also denied that any negotiations were being carried out with delegations from Najaf.
For some time there has been talk in Iraq that a plan exists to break the country into three states; Kurdish in the north, Arab Sunni Muslim in the centre and Arab Shia Muslim in the south.
Dr Dhafir al-Ani, an Iraqi political analyst and former politics professor at Baghdad University, said he would not be surprised if the old rumour proved true.
"Nothing would shock me, we heard of the breakup scenario a long time ago, and it seems that the atmosphere in Iraq nowadays is suitable to carry out any pending agendas."