Italian journalist Giuliana Sgrena has described how she came under a "hail of gunfire" moments after being released from her Iraqi abductors in Baghdad.
Giuliana Sgrena is a veteran war correspondent
Ms Sgrena, who was wounded in the incident, has been sent to a military hospital in Rome for an operation.
She denied US military accounts that the car was speeding past a checkpoint when it was fired upon.
The body of Italian security agent Nicola Calipari, who died in the incident, has now arrived in Rome.
He will be given a state funeral on Monday, and a street in the centre of the city has already been named after him.
US President George W Bush has pledged to fully investigate the shooting.
Ms Sgrena was abducted on 4 February. It is unclear how she was released.
Some Italian press reports say a ransom was paid.
Italy's Prime Minister Silvio Berlusconi, one of President Bush's staunchest allies, has demanded to know why US troops fired on the car carrying Ms Sgrena to safety.
"There was suddenly this shooting, we were hit by a hail of gunfire, and I was speaking with Nicola, who was telling me about what had been happening in Italy in the meantime, when he leaned towards me, probably also to protect me," Ms Sgrena told Rai radio.
"I was especially shocked because we thought that by then the danger was past," she said.
"And then he collapsed and I realised that he was dead."
She said the shooting continued "because the driver wasn't even managing to explain that we were Italian".
"So, it was a really terrible thing."
Asked if the car was going too fast when the US troops opened fire, she said: "We weren't going particularly fast given that type of situation."
This is a serious diplomatic incident between the US and Italy, says the BBC's David Willey in Rome.
President Bush has telephoned Mr Berlusconi to offer his condolences and apologies.
He "assured Prime Minister Berlusconi that it would be fully investigated," said White House spokesman Scott McClellan.
The prime minister and other dignitaries joined family members to welcome Ms Sgrena to Rome's Ciampino airport.
Walking slowly and with some help, a tired Ms Sgrena struggled to a waiting ambulance.
Her left-wing newspaper Il Manifesto says a peace rally will be held in Rome later on Saturday.
Ms Sgrena's colleagues cheered the initial news of her release
The death of one of Italy's most senior intelligence officers in the shooting cast a pall of gloom over what should have been a joyous occasion, says our Rome correspondent.
Mr Calipari is being portrayed as a national hero in Saturday's Italian press for his courage in saving Ms Sgrena's life.
A little-known militant group, Islamic Jihad Organisation, had said it kidnapped Giuliana Sgrena and demanded that Italy withdraw its troops from Iraq.
The same group said in September it had killed two Italian aid workers, Simona Torretta and Simona Pari - but they were later released by another organisation.