Three were detained during raids on homes in south Manchester on Wednesday and one was arrested on Tuesday.
Three men have been arrested in connection with the Manchester concert suicide bombing as a huge investigation into the attack gathers pace. British soldiers have been deployed in place of police officers to guard high-profile sites such as Buckingham Palace and Parliament.
A law enforcement official, speaking anonymously to The New York Times, said Abedi was the son of Libyan immigrants, born in 1994 in Britain. "This attack stands out for its appalling, sickening cowardice - deliberately targeting innocent, defenseless children and young people who should have been enjoying one of the most memorable nights of their lives".
Asked about reports that Abedi had recently returned from Libya, Interior minister Amber Ruddsaid she believed that had now been confirmed.
Abedi, 22, was killed as he detonated an improvised explosive device on late Monday night when thousands of fans were leaving a concert at the Manchester Arena.
"It is a possibility that we can not ignore that there is a wider group of individuals linked to this attack".
Minister Gerard Collomb said Wednesday on BFM television that British and French intelligence have information that Abedi had been to Syria. He did not provide details, and said it's unclear whether Abedi was part of a larger network of attackers. The group had links to Al Qaeda.
Rudd also said Abedi had been known to security services before the bombing. The official also told the Times that Abedi's ID was found at the scene. "The police and security services will be given all the resources they need to complete that task".
"I can't be drawn on that at the moment because it is an ongoing investigation", she said.
Ariana Grande's concerts at London's O2 Arena on Thursday and Friday have not yet been postponed or cancelled.
Sources said the family are from Cheshire.
- The injured - including 12 under the age of 16 - were being treated at eight hospitals across Greater Manchester, Chief Constable Ian Hopkins said.
Officials said all those hospitalized had been identified.
Members of the armed forces will be deployed across Britain under police command, and they would be seen at "big events", according to May.