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 22-year-old is understood to be Manchester-born 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 10.30pm 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 by the coroner 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."
According to officials, 59 people are being treated at eight hospitals across the city.
Several have life-threatening injuries. 12 children under the age of 16 were still being treated and children were among the dead.
A further 60 people were being treated as 'walking wounded'.
Photo: AFP Police officers relocate floral tributes in St Ann's Square in Manchester following the attack at Manchester arena.