Thomas was walking with his girlfriend Christine Delcros across the bridge on Saturday night while visiting London on holiday.
Italian intelligence authorities placed him on watch list, and flagged him to British and Moroccan authorities, according to Corriere della Sera, the Italian daily.
Italy's anti-terrorism police continued to monitor Zaghba for 18 months, "but the evidence was not there that he was a terrorist", Mr Amato said.
The announcement came amid more raids and arrests following the Saturday night rampage - even as officials faced questions about how intelligence services had apparently lost track of at least two suspects before the attack.
Then, his passport and cellphone were sequestered after he tried to board a flight for Turkey with a one-way ticket and a small backpack.
British police on Wednesday said a 30-year- old man was arrested following the London Bridge terror attack which killed seven people and injured 48.
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The actor was surrounded by his family and is said to have died peacefully. "He was bright, witty and fun to work with". He was a graduate of Whitman College in Walla Walla and served in the Army as an announcer on armed forces television.
He said Zaghba was always tracked by Italian intelligence officers while in the country and that United Kingdom authorities were informed. Early accounts suggest Thomas was thrown into the river.
A Spanish victim from Saturday's attack was also confirmed by his family on Wednesday: Ignacio Echevarría, dubbed the "skateboard hero" after witnesses saw him try to protect a woman by fighting off one of the assailants with his skateboard.
Security measures were heightened on Thursday as millions headed out to vote in the general election.
The foreign ministry said in a statement that a third French national was still missing and that four were gravely injured. Echeverria's brother Joaquin told the AP that a diplomatic process had begun for relatives to see the victim's body and to eventually take it back to his native Spain.
Prosecutors ordered the suspect's phone and passport seized, detained him on suspicion of being a foreign fighter on his way to join IS ranks in Syria, and charged him with global terrorism. They worked in the same restaurant: Kentucky Fried Chicken in London's East Ham area.
A man arrested in Limerick in connection with the London terror attacks was released without charge yesterday afternoon.
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