Tuesday's shooting comes just days after Iraq vowed to punish US security firm Blackwater after a probe found that its guards opened "deliberate" fire in Baghdad three weeks ago, killing 17 civilians.
"The government and the prime minister and everybody categorically condemns the actions of this company," the head of the Baghdad security plan, General Qassim Mussawi said in a statement.
"Our weapon is the law for this company and we will try to study this issue calmly."
Witnesses to Tuesday's shooting in the Karrada neighbourhood said a woman taxi driver mistakenly got too close to the firm's convoy and came under immediate gunfire by the guards, who work for Dubai-based Unity Resources Group (URG).
The taxi driver, an Armenian Christian woman identifed as Maroni Ohannes, 49, and a female passenger died of gunshots to the head. Another woman passenger was wounded in the shoulder, while a child was injured by flying glass.
Several witnesses reported barrages of gunfire while a policeman who witnessed the shooting said that after blazing away at the car the foreign security guards sped off "like gangsters."
"The first information that we have is that our security team was approached at speed by a vehicle which failed to stop despite an escalation of warnings which included hand signals and a signal flare," Unity said in a statement.
"Finally shots were fired at the vehicle and it stopped. Unity is now working with the Iraqi authorities to determine the outcome of this incident."
"We deeply regret this incident," the company said.
A small group of grieving relatives of the two dead women, both Christians, gathered for their funerals at the Armenian Church in central Baghdad on Wednesday.
"The incident is a barbarous crime," said one sobbing relative, Kasbar Boghos. "Those guards are inhuman. They have no pity nor do they have any religion."
Another, Kevork Armelian, judged the shootings a "crime against humanity."
"We call on the Iraqi government to put an end to this," Armelian told AFP. "It was clear that women were inside the car when they opened fire haphazardly and deliberately.
"We demand the expulsion of the company so that others can learn a lesson. The Australian government when sending envoys should teach them human rights -- not how to kill innocent people."
A spokesman for RTI International, a non-profit organisation which uses Unity as security escorts in Iraq, said the vehicles were returning to base after dropping off its staff.
"No RTI staff members were involved or present when the incident occurred. Unity was not transporting RTI personnel at the time. They had completed a transportation mission and were returning to their base of operations," Patrick Gibbons, the group's communications director, told AFP.
RTI is involved in training Iraqis in local government management and administration.
A US embassy spokeswoman in Baghdad told AFP that Unity was employed by a non-profit organisation under contract to the US government agency USAID.
"USAID does not direct the security arrangements of contractors. Contractors are contractually responsible for the safety and well being of their employees," spokeswoman Mirembe Nantongo told AFP, adding that the State Department was in contact with the Iraqi authorities about the incident.
Iraq's government said on Monday that it was determined to rein in private security contractors operating in the war-torn country following the Blackwater shooting on September 16, which an Iraqi report said was unprovoked.
"We have set strict mechanisms to control the behaviour of the security companies and their conduct in the streets," interior ministry spokesman Abdul Karim Khalaf said.
Unity Resources Group للخدمات الأمنية واللوجستية في بيان لها من مقرها الرئيس في دبي مسؤولية