Police say investigations were continuing into the identity of the third attacker.
Zaghba "was not a police or MI5 subject of interest", London police said in a statement Tuesday.
Khuram Shazad Butt, 27, was married with two children and lived in east London for a number of years, they said.
The current death toll stands at seven people after three assailants wearing fake suicide vests mowed down pedestrians on London Bridge and launched a stabbing spree in bars in nearby Borough Market.
In Britain's third Islamist attack in as many months, three men on Saturday rammed a van into pedestrians on London Bridge before running into the Borough Market area, where they slit throats and stabbed people indiscriminately.
The officials spoke on condition of anonymity because they were not allowed to discuss details of the case.
Italian news reports said authorities sequestered Zaghba's cell phone and passport when he was stopped at the airport, but that he successfully got them back after a court determined there wasn't enough evidence to accuse him of any terrorism-related crime. Zaghba's Italian citizenship prevented such an expulsion, Italian daily Repubblica said.
Zaghba was reportedly working in a London restaurant and had not been seen in Italy since 2016.
There are now two men in custody while another 12 people held following the attack have since been released.
With the London attack dominating attention, a reduction in the number of police officers in England and Wales by nearly 20,000 during May's six years as interior minister from 2010 to 2016 shot to the top of the election agenda.
Iran FM says Trump reaction to attacks 'repugnant'
One showed a toddler being handed through a first-floor window to safety outside as an armed man looked on. Messages of support were sent by Russian President Vladimir Putin and from the Syrian foreign ministry.
"A 30-year-old man was arrested on suspicion of the commission, preparation or instigation of terrorist acts", police said.
London police chief Cressida Dick said that, while some of the recent attacks in Britain had worldwide dimensions, they had a largely domestic "centre of gravity".
The Islamic State militant group, which is losing territory in Syria and Iraq to an offensive backed by a USA -led coalition, claimed responsibility for the London Bridge attack, though it is unclear whether the attackers had links to the group.
Butt was previously known to police and domestic spy agency MI5 and was a British citizen who had been born in Pakistan, the police said. In a letter posted outside Tuesday, the Ummah Fitness Centre said staff would "help the police in any way we can".
Another neighbour, Michael Mimbo, said Butt supported the north London football team Arsenal. Transport for London confirmed he worked for London Underground in customer services before leaving last October.
Asked whether she regretted presiding over the cuts, May did not answer the question, saying London's Metropolitan Police was well resourced and had powerful counter-terrorism capabilities.
Labour leader Jeremy Corbyn called on Mrs May to quit yesterday, pointing to the loss of 20,000 police jobs, mostly during her six years as interior minister under Mr David Cameron.
But May's own record came under fire from Labour, which - according to opinion polls questioned for their reliability - has closed the gap on her Conservatives ahead of Thursday's election.
The security forces have been raiding addresses in London.
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