Several people who knew Mr. Abedi, including some of his friends, have said that they had warned the authorities about his radical views over the past five years.
Mr. Abedi was barred from Didsbury Mosque, where his family worshiped, after he shouted at an imam who had condemned the ideology of the Islamic State militant group in a sermon, according to Akram Ramadan, a member of the Libyan community in Manchester who attends the mosque.
At least two congregants from the mosque reported Mr. Abedi to the authorities two years ago, the law enforcement official confirmed.
It is highly unusual for the British authorities to publicly confirm the existence of internal investigations into possible security lapses, but the British home secretary, Amber Rudd, welcomed the MI5 review on Monday, saying it was “the right first step” in learning from the Manchester attack.
“There is a lot of information coming out at the moment — about what happened, how this occurred, what people might or might not have known,” Ms. Rudd said in an interview with Sky News on Monday. “And I think it is right that the MI5 takes a look to find out what the facts are.”
She emphasized, however, that while the investigations into possible security failures would be useful, the main focus should be on the terrorism investigation that is also underway.
Detectives investigating the attack said on Friday that they had arrested most of the members of the network believed to have assisted Mr. Abedi on his suicide mission.
The police carried out a series of armed raids across Greater Manchester over the weekend that ended with the arrest of a 25-year-old man in the Old Trafford area. The operation expanded on Monday to Sussex, on the southeast coast of England, where counterterrorism police officers arrested a 23-year-old.
That brought the total number of arrests in the case to 16, the Greater Manchester Police said in a statement on Monday. Of those, two people have been released without charge.
Investigators suspect that Mr. Abedi received extensive training in Libya before returning to Britain, where he is thought to have received assistance from a local network in the days before the attack. The bombing, at Manchester Arena at the end of an Ariana Grande concert on May 22, was Britain’s deadliest since 2005.
“The suspect would have received training abroad, without a shadow of a doubt,” said David Videcette, a former detective for the Metropolitan Police. “To acquire these skills, you can’t sit in your bedroom and watch a YouTube video. It takes practice.”
Initial analysis of the attack pointed to a sophisticated cell that most likely supplied logistical, technical and emotional support to the bomber “in order to keep him in a place where he is willing to blow himself up,” Mr. Videcette said.
While the police have said they believe most of the people in Mr. Abedi’s network have been captured, Ms. Rudd warned on Sunday that some of its members could still be at large. The government has, however, lowed its national threat level to severe — the second-highest level — from critical.
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