"It is a heavy toll that we pay in these attacks", he added. Eight people died and almost 50 were wounded.
The French national was walking with his girlfriend over the bridge when the attack began.
They include a teenager who went to the same gym as Butt who said he was approached to join the Islamic State (IS) group, and a woman who told police she feared he was trying to radicalise children, The Times said.
Seven people were killed on Saturday when three men aboard a white van mowed down pedestrians on London Bridge before slashing and stabbing people at nearby Borough Market, a warren of bars and restaurants. The charges the others face remain unclear.
Questions are being raised about whether British police missed crucial warning signs that could have prevented the attack.
Italian media said authorities took Zaghba's phone and passport but they were returned to him as there was insufficient evidence to accuse him of any terror-related offence.
In an interview with Italy's Radio 24, Mr Giuseppe Amato, the chief prosecutor in Bologna, said Zaghba, an Italian national, had been flagged in March previous year at the Bologna airport en route to Turkey because he was travelling on a one-way ticket with only a backpack as luggage.
Zaghba, an Italian-Moroccan national, was identified as a possible militant threat after he was stopped at Bologna airport in 2016 as tried to reach Syria.More news: WWDC 2017: Apple presents iOS 11 with an AR Kit for Developers
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.
It contains information on thousands of people wanted under the European Arrest Warrant, as well as suspected foreign fighters.
Her family said she would have had "no understanding of the callous cruelty that caused her death".
The latest developments come with counter-terror agencies already facing intense scrutiny after it was revealed another member of the terror gang, Khuram Shazad Butt, 27, had been known to security services.
He was once asked to leave a mosque in east London after "interrupting a Friday sermon".
More details were not immediately available.
The area around Borough Market is not expected to reopen Tuesday.
The fact that Butt was known to authorities before to the attacks has called into question Prime Minister Theresa May's record.
"London stands in defiance against this cowardly attack on our city, our people, our values and our way of life", Khan said in a speech, flanked by politicians from across party divides, police officers and leaders from different faiths.