A plane carrying Sgrena back from Iraq landed on Saturday at Rome's Ciampino Airport, where Prime Minister Silvio Berlusconi was among the dignitaries on hand to welcome her.
Friday's shooting occurred shortly after Sgrena was released after a month being held hostage in Iraq. She left Iraq after being discharged from a Baghdad hospital.
Berlusconi summoned the US ambassador to Rome, Mel Sembler, who met the prime minister for about one hour.
"Given that the fire came from an American source, I called in the American ambassador," Berlusconi said on Friday. "I believe we must have an explanation for such a serious incident, for which someone must take the responsibility."
US President George Bush called Berlusconi and expressed his regret in a five-minute conversation, Bush spokesman Scott McClellan said on Friday night. Bush then assured Berlusconi that the incident would be "fully investigated", he said.
The US military said the car she was riding in after her release was speeding as it approached a coalition checkpoint in western Baghdad on its way to the airport.
It said soldiers shot into the engine block only after trying to warn the driver to stop by "hand and arm signals, flashing white lights and firing warning shots".
The Italian intelligence officer, Nicola Calipari, was killed when he threw himself over Sgrena to protect her from US fire, Berlusconi said. US troops took Sgrena to a US military hospital, where shrapnel was removed from her left shoulder.
Sgrena was expected to be transferred to a military hospital for an operation on her collarbone later on Saturday, the news agency Apcom said.