According to the mother of 22-year-old Zaghba, he became radicalised online, echoing concerns raised by Prime Minister Theresa May that the internet can be fertile ground for breeding extremism.
"We will look at how the processes were followed, what they did".
A third man arrested for carrying out Saturday's deadly attack in London is an Italian-Moroccan who was arrested a year ago on suspicion of trying to reach Syria, Italian sources said on Tuesday.
However, Italy put him on a list of people considered "at risk", as a potential "foreign fighter" and informed both British and Moroccan authorities of his movements, the paper said.
Counter-terror agencies are already facing intense scrutiny after it was revealed Butt had been known to security services.
After the episode in Bologna, Zaghba was monitored by Italian intelligence and was said to have spent short periods of time in Italy, visiting friends and family.
Officials had been searching for a missing French citizen following the attack, and announced Wednesday that they had found a body in the River Thames, reports the Associated Press.
Khuram Shazad Butt was a British citizen born in Pakistan who appeared in a television documentary previous year about extremists in Britain.
Roland-Garros: EN DIRECT
Rafael Nadal a séchement battu Stan Wawrinka en trois sets (6-2, 6-3, 6-1), dimanche 11 juin , en finale de Roland-Garros. L'Autrichien a fini en charpie, comme les autres, essoré en deux heures et trois sets avec un 6-0 comme cadeau d'adieu.
Material from the Associated Press was used in this report.
The suspect, identified as a 30-year-old man, was arrested on suspicion of "commission, preparation or instigation of terrorist acts", the Metropolitan Police said in a statement early Wednesday.
Rachid Redouane, who police said claimed to be Moroccan and Libyan, also went by the name Rachid Elkhdar with a different date of birth.
At least seven people were killed and another 48 people were wounded in the attack.
The investigation into Butt involved a "full package" of investigatory measures.
Eighteen plots have been stopped since 2013, including five since the Westminster attack.
After the ISIS called for attacks in the West in September 2014, the British security services grew increasingly concerned that al-Muhajiroun members, who had remained in the United Kingdom, would carry out terrorist attacks.
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