Butt and his two accomplices drove a hired van into pedestrians on London Bridge before stabbing people in the area around Borough Market in an attack which began at 9.58pm BST.
Two Australians were among the seven killed in a van and knife attacks on and on Saturday.
British security and law enforcement officials are investigating Butt as the potential ringleader of the cell, according to a security official who spoke on condition of anonymity because he was not authorized to discuss the ongoing details.
The report said that Italy had put him on a watch list and flagged his presence to Moroccan and British authorities.
Of the 3,000 people, only "a tiny proportion" are placed under 24-hour surveillance if they are suspected of planning an attack.
Italian prosecutor Giuseppe Amato said there was not enough evidence to arrest or charge the 22-year-old when he was caught at Bologna airport last year.
As the debate rages over security, the British police yesterday named the third person in the weekend attack as Youssef Zaghba, 22, believed to be an Italian national of Moroccan descent.
Pakistani Butt was named as one of the London Bridge terrorists yesterday by Met police.
Police searching for a French man who has been missing since the London Bridge attack say they have recovered a body from the River Thames.
London police have arrested another man suspected of a connection to the lethal attack on London Bridge.
The Islamic State claimed Sunday to have been behind the attack.
Police name 2 suspects of London Bridge attack
Volunteer your time and labor or donate to a homeless shelter. "I could tell you that I was devastated", he told Postmedia. Forty-eight people were taken to hospital and 18 are in critical condition, according to the latest police update.
His case was not prioritised because he was viewed as representing a medium threat, the category of people mixing with extremists but not having done anything to suggest they planned an attack.
Counter-terror agencies are already facing intense scrutiny after it was revealed Butt had been known to security services. Authorities said he aroused suspicion because he tried to board a flight to Turkey with a one-way ticket and a small backpack.
Corriere said Zaghba had been radicalized by Khuram Butt, considered the head of the cell. The police have not yet been able to identify the third man.
Bilal Dar told The Associated Press in the Pakistani city of Jhelum that his cousin, Khurum Butt, lived in the city until he was about 7 years old.
The married father-of-two, who worked for London Underground as a trainee customer services assistant for almost six months past year, could be seen in the programme arguing with police officers in the street, after displaying a flag used by so-called Islamic State in a London park.
The news raises questions about the police's judgment and increases pressure on Prime Minister Theresa May, who three days before a national election is facing criticism for overseeing cuts to police during her years as interior minister.
Her remarks came following a poll published earlier yesterday by the group Survation which showed Mrs May's lead over the opposition Labour has shrivelled to just over a single point - 41.6 per cent to 40.4 per cent.
"Counter-terrorism funding is ringfenced but cuts to the general policing budget have impacted on neighbourhood policing teams in many parts of the country including London", The Guardian quoted him as saying.
The assailants ran people over on London Bridge before lunging seemingly at random at the crowds gathered around Borough Market, which is full of restaurants and bars.
Commuters walk across London Bridge, with new security barriers, after work in London, Tuesday, June 6, 2017.
A minute's silence was observed in Britain at 11 a.m. local time in memory of those killed during the attack.
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