Earlier on Tuesday, another man, originally from Morocco, was arrested in Limerick city, but he was released by afternoon, Xinhua news agency reported.
He was arrested by the Special Detective Unit, which deals with terrorism.
Zaghba, Pakistan-born British citizen Khuram Shazad Butt, 27, and Rachid Redouane, 30, who claimed to be Moroccan-Libyan, launched a murderous rampage around London Bridge and Borough Market on Saturday night.
He's the second person taken into custody in Ireland over Saturday's atrocity.
However, Gardaí have stressed their investigation is focused on theft and fraud offences rather than terror. He was identified after a documentation check in Britain found he had lived in south Dublin for some time. He used public libraries and used his own name, addresses and phone number when registering in at least three.
Police on Tuesday named the third assailant killed along with Redouane and Khuram Butt by armed police on Saturday as Youssef Zaghba (22), a Moroccan-Italian man who had been placed on an Italian counter-terrorism watch list and stopped by them from travelling to Syria a year ago.More news: SpaceX's resupply mission to ISS on course for Saturday launch
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Corriere wrote that Zaghba was stopped at Bologna airport in 2016 when he was trying to fly to Syria and that Italian authorities had tipped off Britain about his movements.
The Metropolitan Police said all of the 15 victims now in critical care had been identified, as public appeals continued for several people who have not been located since the attack.
London Mayor Sadiq Khan stands side-by-side with the chief of London police, Cressida Dick, to condemn attack at London Bridge, in which seven people were killed. Butt was revealed as an extremist in a Channel 4 documentary.
The investigation into Redouane's time in Ireland has intensified over the past 48 hours.
He left the country at some point and is believed to have lived in Ireland again in 2015. Gardaí believe his last visit to Ireland was early a year ago.