Kobold told reporters on Friday that Gandolfini's body has been released to a funeral director and that the actor's family was working with the Italian government to get through red tape in order to get the body back to the United States as soon as possible.
This process can take up to 10 days, but Kobold said the actor's family was hoping to have the body back in the U.S. by mid-week. A funeral is tentatively planned to take place June 29 in New York, at the latest.
Gandolfini died Wednesday night. His body was discovered in a Rome hotel room by a family member. He was 51 years old.
He had arrived in Rome Tuesday and spent the day with his son. They visited the Vatican and dined in the hotel. They also dined together Wednesday night as they waited for the arrival of Gandolfini's sister, Leta.
Asked if Gandolfini had a history of heart problems, Kobold said he was healthy.
"There's nothing out of the ordinary. It was a heart attack. It was a natural cause," he said. "There was no foul play, no substance abuse. None of that."
On Thursday, Dr. Claudio Modini, head of the emergency room at the Policlinic Umberto I hospital in Rome, said the actor suffered a cardiac arrest. Sudden cardiac arrest can be due to a heart attack, a heart rhythm problem, or as a result of trauma.
Leta went to the morgue on Friday to formally identify the body.
Gandolfini was to have helped preside over the closing ceremony on Saturday of the Taormina Film Festival in Sicily. The festival instead is organizing a tribute to him.
His portrayal of criminal Tony Soprano in HBO's landmark drama series "The Sopranos" was just one facet of his rich legacy as an actor in movies and plays.
The Associated Press contributed to this report.