Prime Minister Silvio Berlusconi also told lawmakers on Wednesday that the car carrying agent Nicola Calipari and a just-liberated hostage was travelling slowly and stopped immediately when a light was flashed at a checkpoint, before US troops fired on the car.
In a carefully worded address - his first major speech since the shooting - Berlusconi said Italy had the duty to demand the truth about Friday's shooting from its US allies.
"I'm sure that in a very short time every aspect of this will be clarified," he said.
The idea that Calipari was killed by friendly fire is painful to accept, the premier said. But he reassured lawmakers: "The United States has no intention of evading the truth."
Berlusconi is a staunch supporter of US President George Bush and the US-led campaign, and has been struggling to balance his decision to keep 3000 troops in Iraq against heavy anti-war sentiment in Italy.
Lawmakers followed the speech with a standing ovation in Calipari's honour.
The 20-minute address did not mention whether ransom was paid to win the release of journalist Giuliana Sgrena.
Some Italian officials have suggested money changed hands, but there has been no official confirmation. Foreign Minister Gianfranco Fini denied the suggestions on Wednesday.
Calipari was shot by US forces
while escorting a freed hostage
"There has been no payment," he said during a talk show on RAI1 state television.
Giving Italy's version of the shooting, Berlusconi said Calipari had notified an Italian liaison officer, waiting at the Baghdad airport along with an American officer that he was on his way with Sgrena.
However, the top US general in Iraq has said he had no indication that Italian officials gave advance notice of the route the Italians' car was taking.
In a statement released after the shooting, the US Army's 3rd Infantry Division, which controls Baghdad, said the vehicle was speeding and refused to stop.
The statement also said a US patrol tried to warn a driver with hand and arm signals, by flashing white lights and firing shots in front of the car.
"The case of friendly fire is certainly the most painful to bear. It feels like an injustice beyond any sentiment. It's something unreasonable," Berlusconi said.
Photos aired by RAI, state TV's main evening news programme, showed the light grey Toyota Corolla that Calipari and Sgrena were riding in, which is still in Iraq in the hands of the US military.
"The case of friendly fire is certainly the most painful to bear. It feels like an injustice beyond any sentiment. It's something unreasonable"
Italian prime minister
The body of the car appeared to have little or no damage on its left side and front, including the lights. A few bullet holes are visible on the right side - near the wheel and the front door.
Inside, the seats appear to be covered in glass, although the photos of the interior are grainy. A bullet hole is also evident in the back seat on the left side, where Sgrena reportedly was sitting.
US officials have said American troops fired at the car's engine to stop it.
The office of Italian President Carlo Azeglio Ciampi said on Wednesday that Bush had sent him a letter renewing a promise for a swift and thorough investigation.
In it, Bush called the shooting a "terrible tragedy" and expressed his solidarity, Ciampi's office said.
US-led forces in Iraq announced on Tuesday that they were ordering an investigation into the shooting, to be led by a US brigadier-general with Italian officials' participation.
Berlusconi said he expected the joint commission to release its findings in three to four weeks.