Authorities have said Salman Abedi, the 22-year-old suspected suicide bomber who died in the explosion, grew up in an area near Moss Side.
Before arriving at the concert, which had attracted a young audience including many children, Abedi is believed to have put the final touches to his bomb in a city centre flat.
"This is still a live investigation which is not slowing down", police said.
The threat assessment has now been returned to the level it was at prior to the attack in Manchester, northwest England, and means soldiers who have been assisting police would be withdrawn from Britain's streets from midnight on Monday.
The Chief Constable of Greater Manchester Police, Ian Hopkins, said 12 locations were still being searched.
"In any case, the links with Daesh are proven", he said, using a term for ISIL.In the wake of the attack, the UK's terror threat level was raised from severe to critical, meaning another attack is imminent.Armed troops have also been sent to guard key sites, a rare sight in mainland Britain.
A total of 10 arrests have been made, but a 16-year-old boy and a 34-year-old woman have been released without charge, police said.
Those who were most tragically affected, Grande said, "will be on my mind and in my heart everyday and I will think of them with everything I do for the rest of my life".
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Former U.S. President Barack Obama offered his condolences to the victims and support for those wounded in the Manchester bombing during a meeting Saturday with Prince Harry at London's Kensington Palace. "We can't let the terrorists win by dissuading us from going about our normal business".
Associated Press writer Jill Lawless reported this story from London and AP writer Mstyslav Chernov reported in Manchester. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
Meanwhile, heavy armed presence is being rolled out for what is termed as a Bank Holiday weekend in the United Kingdom - an annual holiday on Monday making it a weekend packed with lots of public events.
The arrests bring to 11 the number of suspects held in Britain over Monday's blast at a concert by U.S. pop idol Ariana Grande, in which 22 people died and 116 were injured, and for which the Islamic State group has claimed responsibility.
Sixty six people injured in the attack were still in hospital, she added.
However, the Prime Minister stressed that the "country should remain vigilant" during the hundreds of events taking place over the coming days - including the FA Cup final at Wembley, and the Premiership Rugby final at Twickenham.
Police lined the street as an athletic event went ahead in Manchester four days after a suicide bomber targeted the city's arena.
She took to Instagram to share a powerful message with all her fans, and to share her intentions of holding a benefit concert sometime in the future, although an official date for that has not yet been released. We will not quit or operate in fear.