Police have released surveillance-camera images of Abedi on the night of the attack that show him dressed in sneakers, jeans, a dark jacket and a baseball cap.
"We are especially keen to find out why he kept going back to the Wilmslow Road area and we need to find the blue suitcase which he used during these trips", he said.
'I want to stress that this is a different item than the one he used in the attack.
He said they have no reason to believe the case and its contents contain anything unsafe, but would ask people to be cautious.
Greater Manchester Police said two men aged 20 and 24 from the Fallowfield area and a 37-year-old man from the Blackley area had been released.
MI5 launched a "post incident investigation" into how Abedi was overlooked by the service, the BBC said Monday, as a second, separate inquiry was undertaken for ministers and others who oversee MI5's work.
There have previously been searches in Manchester, Chester and Shoreham-by-Sea in West Sussex, where a 23-year-old man was arrested early Tuesday (AEST) in relation to the bombing.More news: UK police arrest eleventh suspect of Manchester terror attack
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Abedi, whose parents come from Libya, is thought to have received terror training in the country before returning to the United Kingdom just days before killing 22 people.
MANCHESTER bomber Salman Abedi was known to police for a "relatively minor" criminal record, but not for holding extremist views, it has been revealed.
Host Mike Sweeney asked him: 'Just to clarify, the reports you have got were to do with behaviour that was more associated with criminal behaviour rather than reports about his viewpoints being extremist?'
It was revealed last week that Abedi, 22, was in a pool of former "subjects of interest" whose risk remained "subject to review" by MI5 and partner agencies.
Manchester City Council has called a vigil in the centre of the northwest England city for 2131 GMT - the exact moment that Abedi detonated his bomb outside a pop concert by teen idol Ariana Grande in one of Europe's biggest indoor arenas.
Home Secretary Amber Rudd yesterday refused to comment on whether opportunities were missed to spot the murderous intent of the 22-year-old before his deadly attack.
On Saturday, Britain lowered its official terrorism threat level from "critical" to "severe" after police said they had dismantled a large part of Abedi's network.
His father and younger brother, Hashem, have been taken into custody by Libyan authorities.