Italy's foreign minister has demanded the US "identify and punish" those responsible for the death of an Italian intelligence agent in Iraq.
Calipari has become a national hero in Italy
Gianfranco Fini said the US and Italy had different versions of what happened to Nicola Calipari, who died under US fire while escorting a freed hostage.
The US says shots were fired because the vehicle was speeding and did not heed troops' warnings for it to stop.
But Mr Fini said the car was travelling at no more than 40km per hour.
Calipari had also made "all the necessary contacts" with US and Italian officials about the hostage's release and the journey to the airport, he added.
The incident has intensified the already strong Italian opposition to the country's military presence in Iraq and put intense pressure on Prime Minister Silvio Berlusconi's government to find answers.
The BBC's Tamsin Smith in Rome says Mr Fini's comments, which have pre-empted an investigation into the incident, were very much for domestic consumption.
Political observers in Rome say there is a serious problem of jurisdiction in any attempt to bring criminal proceedings, as the shooting took place in an area under US military control in a third country.
Calipari has become a national hero in Italy, and thousands came out onto the streets on Monday to applaud the funeral cortege.
'Truth and justice'
Mr Fini said the vehicle carrying the released hostage and agents was well-lit to facilitate checks.
However, it stopped after a powerful light was shone on it from the roadside and the shooting began immediately, without warning, he said.
US: Forces fired on a vehicle that was approaching at high speed
Troops attempted to warn the driver to stop by hand and arm signals, flashing white lights, and firing warning shots
When the driver didn't stop, the soldiers shot into the engine block
Sgrena: The driver had spoken twice to the embassy and to Italy to say we were on our way to the airport
We were less than a kilometre [from the airport]... when... I remember there was shooting
The driver began screaming that we were Italian
We weren't going particularly fast given that type of situation
A volley of shots from automatic weapons followed, lasting 10-15 seconds, the foreign minister added.
The occupants of the vehicle were only identified by a second agent who was pulled from the car alive, he said.
Mr Fini did, however, reject the allegation made by freed hostage Giuliana Sgrena that the car was deliberately targeted as "groundless".
"We ask for truth and justice," he said. "We hope that within the next few hours this affirmed wish for loyal co-operation will yield its first major concrete result."
"We hope that this is not an opportunity to whip up political campaigns and to sow anti-American sentiment in public opinion, which certainly have no reason to exist."
Tuesday's Washington Times newspaper quoted a Pentagon memo as saying the Italian security forces appeared to have made no prior arrangement for Ms Sgrena's transfer to the airport.
It added that US troops are trained to fire on erratic speeding vehicles, a description which corresponds to the US version of events.
"This is war," the memo was quoted as saying. "About 500 American service members have been killed by hostile fire while operating on Iraqi streets and highways."