The intelligence agency is reviewing whether more could have been done to prevent Salman Abedi from detonating his nail bomb last week which killed 22 people and injured dozens more.
The domestic security service is said to be investigating if there were any errors made in the handling of intelligence concerning the bomber responsible for last Monday's attack.
Spy chiefs are believed to have held an emergency review in the days after the atrocity, while a separate in-depth inquiry is being conducted to look at the decision making surrounding his case before the massacre.
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Amber Rudd backs MI5 Manchester bombing inquiry after 'missed warnings' over Salman Abedi
The intelligence services are still collecting information about him and about the people around him
Concerns have been raised that a series of warnings about Abedi, including from family members, were not acted upon.
And there have been reports that the temporary exclusion orders (TEOs), which are intended to control jihadis movements, have only been used once.
A senior Whitehall source previously revealed the mass murderer Abedi was a "former subject of interest" to the security services whose risk "remained subject to review".
The intelligence agency is reviewing whether more could have been done to prevent Salman Abedi
Early this year, the FBI warned UK security chiefs that the the Libyan-born Islamist was planning an attack on British soil, according to the Mail on Sunday.
The 22-year-old's father Ramadan and brother Hashim have been detained in Libya and another brother, Ismail, was arrested in Manchester on Tuesday.
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Before his arrest, Ramadan Abedi rejected claims he was a member of the Libyan Islamic Fighting Group, but added that he supports the organisation, which is banned in the UK.
In the translated interview, shown on the BBC, he protested his son's innocence, saying: "I'm sure that Salman didn't carry out such an act."
Police searching a property in Manchester in connection with mass murderer Salman Abedi
But the killer's sister said she believed her brother may have been reacting to US-led strikes in the Middle East.
Abedi travelled through Istanbul in Turkey and Dusseldorf in Germany in the days before the attack, a Turkish official said.
Ms Rudd has already confirmed Abedi had recently returned to the UK after a visit to Libya.
She said: "The intelligence services are still collecting information about him and about the people around him.
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"But I would not rush to conclusions, as you seem to be, that they have somehow missed something."
Ms Rudd said she cannot demand that a certain number of TEOs are used, but to make sure the security service has the "tools they can use" to protect the public.
She said: "We need to put our efforts into protecting young people.
"People in our communities who are being targeted by Daesh [the Islamic State terror group] and fed a false ideology."
She added that the government had "never understated" the terror threat to the UK.