Salman Abedi has been named by police as the suspected suicide bomber who killed 22 people and injured 59 at Manchester Arena on Monday night.
The BBC understands the 22-year-old was Manchester born and from a family of Libyan origin.
So far three victims have been named – Saffie Rose Roussos, eight, Georgina Callander and John Atkinson, 28.
Greater Manchester Police said the priority was to establish whether Abedi had worked alone or not.
Abedi is thought to have blown himself up in the arena’s foyer shortly after 22:30 BST on Monday, as fans were beginning to leave a concert by US singer Ariana Grande.
Abedi, who had at least three siblings, had lived at several addresses in Manchester, including a property at Elsmore Road, Fallowfield, which was earlier raided by police.
Greater Manchester Police Chief Constable Ian Hopkins said searches at two addresses had been carried out, including the one in Fallowfield, where a controlled explosion had been used to gain “safe” access.
He said Abedi had not been formally identified and so would not comment further.
Mr Hopkins passed on “heartfelt sympathies to all the innocent people caught up in last night’s despicable act”, adding that specially-trained family liaison officers were supporting families.
“There has been much speculation and names of those who may have been killed in the media and social media,” he said.
“We accept that this is inevitable, however, we ask that people allow the police and coroner to release the names once the families are ready and appropriately supported.”