A confidential report obtained by ABC News from the U.S. Embassy Baghdad said five Blackwater security guards were involved in the firefight when a car bomb went off northwest of the Green Zone.
The report said that subsequent car bombs went off and that a firefight erupted, adding that the fight involved Iraqi police units.
None of the Blackwater security guards can be prosecuted in Iraqi courts because of a law passed by the U.S.-led Coalition Provisional Authority.
"They should not have immunity," Dabbagh said. "We don't want them to leave Iraq … but we need to keep them accountable."
ABC News reported Tuesday that President Bush has personally ordered his top national security officials to get to the bottom of what happened.
Defense Secretary Robert Gates has also ordered a comprehensive review of the U.S. government's use of security contractors in Iraq.
The incident has effectively grounded U.S. Embassy officials in Baghdad — who rely on Blackwater's private security forces to get around — from visiting Iraqi leaders and ministries.
During a congressional hearing last week, U.S. Ambassador to Iraq Ryan Crocker testified that the United States has become dependent on private security firms in Iraq.
"There is simply no way at all that the State Department's Bureau of Diplomatic Security could ever have enough full-time personnel to staff the security function in Iraq," Crocker said. "There is no alternative except through contracts."
Blackwater, based in Moyock, N.C., has more than 1,000 personnel in Iraq. Most of those security guards protect senior American diplomats in Iraq and others.
Statistics vary on how many private security guards are operating in Iraq. A recent Congressional Research report said there are as many as 30,000 security workers in Iraq.
However, a trade group in Washington that represents Blackwater and other companies in Iraq put the figure somewhere closer to 20,000 private guards.
Doug Brooks, president of the International Peace Operations Association, said on public television Tuesday that most of the private security forces in Iraq are Iraqi. Only 2,000 are American, he said.
Critics of the Iraq War say the incident has brought to light how reliant the U.S. government has become on private firms, even in war zones.
"Blackwater is the realization of former Secretary of Defense Donald Rumsfeld's vision of a 'hollow military' where everything that can be privatized and outsourced, will be," author Naomi Klein said in an interview with ABC News.
Klein, who is promoting her new book, "The Shock Doctrine," argued the Bush administration has allowed private contractors to "gorge" on Iraq. She said the Bush administration has created a "parallel army" in Iraq of private contractors who are not held to the same rules as the U.S. military.
"That's what's been happening in Iraq. You have this corporate mission creep. As the war spirals, you have private companies taking on a larger and larger role," Klein said.
Klein said Americans only learn about how reliant the U.S. government is on private corporations when there is a crisis or incident, such as the Blackwater investigation and the Abu Ghraib scandal involving interrogators from a private intelligence firm called CACI.
Four in 10 Iraqis, and half of Baghdad residents, report "unnecessary violence against civilians" by U.S. or coalition forces in their local area, according to an ABC News poll of Iraqis that was released in September.
With reporting by ABC News' Brian Hartman in Iraq, Jonathan Karl, Luis Martinez and Kirit Radia.