Youssef Zaghba, a Moroccan-Italian, was the third man shot dead by police during Saturday's terrorist attack in central London, Italian security officials told POLITICO.
A property in Ilford, east London, was also searched by police at about 01:30 BST, but no arrests had been made, the police said.
Italy's main media outlets said Youssef Zaghba had an Italian mother from Bologna and a Moroccan father.
The Scotland Yard said one of them was Khuram Shazad Butt, 27, a Pakistan-born individual who had been investigated by MI5 and United Kingdom police.
Dozens of people gathered in driving rain at the end of London Bridge, where a growing mound of flowers sits beside a police cordon. The attackers were shot dead by police.More news: Jeff Sessions offered to resign after rising tension with Trump
Police have arrested at least 14 people in connection to the attack, though most have been released without charge.
But Butt, 27, was not the typical resident of the East London neighborhood of Barking.
The second alleged attacker was identified by police as Redouane, who alternately used the surname Elkhdar, and claimed to be Moroccan and Libyan.More news: Tamim century lifts Bangladesh to 305-6 against England
At any one time there are around 500 active counter-terrorism investigations concerning 3,000 people of interest.
The first victim has been named as Chrissy Archibald, a Canadian bride-to-be who volunteered at a homeless shelter. More than 40 people were injured in the attack.
Ms Delcros was seriously injured by the van, although her condition in hospital has stabilised, her family said.
A French national was also killed in the attack, according to foreign minister Jean-Yves Le Drian, which the BBC understands to be Mr Pigeard.
"One unconfirmed report suggests that did happen, apparently when Zaghba arrived at Stansted Airport in January - but that border staff still let him in", he said.More news: Novak Djokovic loses in French Open 2017 quarterfinals to Dominic Thiem