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 was Manchester born and from a family of Libyan origin, the BBC understands.
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.
A vigil is being held in front of the town hall in Manchester’s Albert Square.
‘Vigil for peace’ at Manchester’s Albert Square
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.
Greater Manchester Police Chief Constable Ian 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.
Eight-year-old Saffie Rose Roussos was a pupil at Tarleton Primary School, in Lancashire.
Her head teacher, Chris Upton, said she had been “simply a beautiful little girl in every aspect of the word” and was “loved by everyone”.
John Atkinson was from Bury in Greater Manchester.
Student Georgina Callander, believed to have been 18, has also been named as among the dead.
She had been studying health and social care at Runshaw College in Leyland, Lancashire.
The wounded are being treated at eight hospitals around the city, with 12 children under the age of 16 among them.
Several people are still missing, including teenagers Laura MacIntyre and Eilidh MacLeod, from Barra in the Outer Hebrides, 15-year-old Olivia Campbell, Chloe Rutherford, 17, and Liam Curry, 19.
Scotland’s First Minister Nicola Sturgeon said police were in contact with Laura and Eilidh’s families, adding: “It is hard for any of us to imagine the anguish that their families are going through right now.
“They are in our thoughts.”
In a statement in Downing Street on Tuesday, the prime minister said the bombing had been a “callous terrorist attack” that targeted “defenceless young people”.
Number 10 later said Mrs May – who is now in Manchester – had been updated “through [Monday] night” and had phoned Labour leader Jeremy Corbyn at 04:00 BST to brief him.
It is the worst terrorist attack in the UK since the 7 July bombings in 2005, in which 52 people were killed by four suicide bombers
So-called Islamic State has said – via IS channels on the messaging app Telegram – it was behind the Manchester attack, but this has not been verified.
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Source: BBC