Born in Britain to Libyan parents, Abedi is believed to have returned from a trip to Libya a few days before the bombing.
Investigators said he bought most of the core components of the bomb himself and was often alone in the days leading up to the attack. This image was taken from CCTV in the city centre on 22 May.
As well as the CCTV image of Abedi, detectives have released a picture of a replica case, as they continue to piece together the terrorist's movements in the lead-up to the attack.
"We have no reason to believe the case and its contents contain anything unsafe, but would ask people to be cautious", he continued. Where did you see him with it during that time?
A bomb disposal unit was deployed at the scene as a precaution but was later stood down, while a police cordon remained in place. Police are keen to talk to anyone who saw him. "This has led us to the Banff Road area in Rusholme", Jackson said.
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. In the future, we can look at anything else that might need to be done.
"But I would not rush to conclusions, as you seem to be, that they have somehow missed something".
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"Our response to this violence must be to come closer together, to help each other, to love more, to sing louder and to live more kindly and generously than we did before", she wrote.
However, police have said they are continuing to work around-the-clock to identify all of those behind the deadly terror attack.
Chief Constable of Greater Manchester Police Ian Hopkins said the suicide attacker appeared on police logs in 2012 for theft, receiving stolen goods and assault.
Police have arrested 16 people since.
The 37-year-old landlord is believed to be one of three men released without charge on Tuesday, alongside two men aged 20 and 24 said to be Abedi's cousins.
The bombing investigation expanded early Monday when police arrested a 23-year-old man on the south coast of England, hundreds of miles south of Manchester.