They are accusing the militias, which they say are backed by neighbouring Iran, of carrying out irresponsible and provocative acts.
These militia - Thaaru Allah (Revenge of God), Hizb Allah (Party of God) and the Badr Brigades - are charged with crossing the Iranian border after the occupation of Iraq last April to conduct a campaign of fear on the local people.
Victims speak out
One such victim is Dr Mahdi Khalaf. Dr Khalaf, who holds a PhD in lexicography, spoke to Aljazeera.net spoke in Dubai, UAE. He says he was forced to leave his city because his daughters were unable to continue their university studies amid continuous harassment by the militias.
"These men are not Iraqis. They are dishonourable people," he said. "They arrested my daughters and insulted them by describing them as infidels because they are Sunnis," Dr Khalaf said.
"Iraqis do not think this way; it is an ideology of extreme Iranian Shia clerics."
Armed members of the Badr
Brigade militia control crowds
One Iraqi living in self-imposed political exile, who spoke to Aljazeera.net on condition of anonymity, said his 55-year-old sister had been arrested by a Shia militia in Basra and suffered physical and psychological damage because of "sadistic" practices used on her while in detention.
"She is a grandmother, but her age was not enough to trigger her captors' kindness," he said. "They insulted her, they told her awful things.
"They arrested her because she was a Baathist Sunni school-teacher ... people of Basra do not know who authorised these militias to condemn this and convict that. It is a mess.
"My sister was released after I talked to high-ranking Iranian-backed Shia figures and told them not to play this game with me and my family because I know a lot about them.
"She was released and is now in Baghdad preparing to leave Iraq for good."
Yusuf al-Musawai, the secretary-general of Thaaru Allah, said his group did not kill Baathists or Saddam Hussein loyalists, but confirmed that his group is committed to wiping out criminally culpable officials of the former government.
"It is our responsibility to eliminate symbols of the former regime, but not through assassination," al-Musawai said. "We arrest officials accused of committing crimes against Iraqi people, we interrogate them before sending them to the Iraqi police. We do not deal with coalition forces."
Shia cleric Muhammad Baqir
al-Hakim formed Badr in Iran
Director of the Basra Internal Security Department, Colonel Muhammad Kadhim al-Ali, confirmed that dozens of Saddam loyalists have been killed in recent months.
"Dozens of political assassinations have taken place in Basra," al-Ali said.
"Former officials accused of committing crimes against the Iraqi people have been killed in Basra," he said. He refused to reveal the identity of the assassinators.
It is not the first call by Iraqis to save Iraq's second largest city from the aggravations of extreme armed Shia militias.
On 4 January 2004, 200 Iraqi intellectuals and politicians met in London and issued a statement in which they appealled to the US-appointed Iraqi Governing Council (IGC) and Iraq's religious authorities to stop terror caused by armed Shia militias in Basra.
The statement named Thaaru Allah and Hizb Allah and accused them of intimidating schoolgirls, forcing Muslim and non-Muslims women to wear the hijab, killing Christian alcohol dealers, and attacking restaurants that serve alcohol.
The people of Basra say the militias consist of thousands of young men commanded by Shia clerics. But the real nationality and background of the members is disputed. Iraqis claim that they are Iranians, while militia leaders claim they are Iraqis.