Although detectives have no reason to believe the luggage contains anything unsafe, they warned the public not to approach it and instead call 999 immediately.
Pope Francis is urging prayers for the victims of the Manchester concert attack and has denounced how "so many young lives were cruelly broken".
Mr Jackson said officers had been conducting house-to-house inquiries but were "still not satisfied" why Abedi went there and said it was "vital" they understood exactly where he went and who he spoke to in the final days before the attack.
The suitcase was not used in the attack, which was carried out when Abedi detonated an improvised bomb minutes after the concert ended, Greater Manchester Police Detective Chief Superintendent Russ Jackson said.
Investigators have been attempting to piece together Abedi's movements between when he arrived back in Manchester from Libya on 18 May, and the bombing four days later.
Councils and funeral directors have refused to deal with Salman Abedi's body as it emerged his corpse is now being kept at a morgue outside Manchester.
New CCTV footage has emerged that appears to show Abedi shopping at a convenience store.
Abedi had a "relatively minor" criminal record as a teenager but was not known to police for holding extremist views. ISIS has claimed responsibility for the atrocity.
London attacks: Three more arrested, say police
The BBC reports that Thomas was last seen on London Bridge walking with his girlfriend, who was seriously injured in the violence. He flashed the torch at me and shouted "get inside, get inside". "The suspect was then cuffed and taken to a police vehicle .
The FBI warned United Kingdom security chiefs that Abedi was planning an attack on British soil, according to the Mail on Sunday.
He told me, but I can't quite remember what he said, he was from Libya.
"We continue to appeal for the public's help in tracking Abedi's movements. As a first step, it is absolutely right". "We shouldn't rush to make any conclusions at this stage".
In a BBC television interview on Sunday, Rudd was quizzed over whether MI5 has the resources to keep on top of the terror threat.
A British counterterrorism official told CNN it was not clear whether Abedi received training with ISIS in Syria.
In a statement after the attack, Grande said "we won't let this divide us". Police are keen to talk to anyone who saw him.
The source told Reuters that Abedi was not among the 3,000 people now under active investigation by MI5, although he was one of around 20,000 people known to the agency, whose focus is on countering terrorism and espionage.The BBC said MI5 was alerted at least three times to the "extremist views" of Abedi, a 22-year-old who grew up in Manchester in a family of immigrants from Libya.
This runs counter to the impression given so far in the investigation, which has seen 16 arrests.
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