Iraqi Trade Minister Abdul Falah al-Sudany on Thursday expressed outrage over the killing, and a spokesman for him said trade ties could be cut if Australia does not apologise and pay compensation.
The soldiers mistook the armed bodyguards, dressed in civilian attire, for insurgents and opened fire, killing one and wounding three, earlier this week.
"The minister holds the Australian government responsible and demands an apology and payment of compensation. If this does not happen he will reconsider trade agreements between the two countries," his spokesman Muhammed Hanoun told Reuters on Thursday.
Mr Howard said it is too early to apportion blame or bow to demands for an official apology.
"I am very sorry that a man lost his life ... but until I know what's happened it's not appropriate to be flinging out (formal) apologies," he told the Nine Network.
Mr Howard said he had received assurances from the Iraqi government early on Friday that the incident would not jeopardise trade deals between the two countries.
Australia had received those assurances after Trade Minister Mark Vaile wrote to the Iraqi government, he said.
"I can tell you a short while ago ... the Iraqi trade minister told our ambassador that he greatly appreciated the letter which Mark Vaile had sent to him and that he did not want this incident to interfere with the bilateral relationship or to affect our trade relationship," Mr Howard said. "It's a sad incident but let's not overreact."
Australia's ambassador in Iraq, Howard Brown, met with Mr al-Sudany overnight, and conveyed Australia's regret over the incident, according to Mr Vaile.
The Vice-Chief of the Australian Defence Force, Lieutenant-General Ken Gillespie, said the ADF deeply regrets the loss of life and injuries, and an investigation has been launched.
Defence Minister Brendan Nelson had no official comment, telling reporters on Thursday to direct their questions to the ADF.
Foreign forces including Australian troops have started pulling out of the southern al-Muthanna province.
The 450 Australian troops will be redeployed 80km from their current base at Camp Smitty, to the US airbase at Tallil, outside the city of Nasiriyah in neighbouring Dhi Qar province, where they will train Iraqi security forces and help with reconstruction work.
Hostages freed
Meanwhile, the kidnappers of more than 100 Iraqi government employees freed a Sunni and female hostages, however about 40 to 50 remain captive.
The workers were seized from a bus north of Baghdad after finishing work at a factory.
Those still held captive are believed to be Shi'ites from Baghdad's Sadr City and the neighbourhoods of Shuala and Hurriyah.
A separate report said Iraqi police stormed a farm and freed 17 of the hostages.