Police said they could not rule out that the Libyan was part of a wider network, but after seven days of investigation involving 1,000 officers and "hundreds" of witnesses, they concluded that he mostly acted alone.
The Manchester Evening News claimed that Abedi's remains were being kept at a morgue outside the Greater Manchester area.
Manchester Central Mosque said it would not have anything to do with Abedi, who killed 22 people when he bombed Manchester Arena last Monday night, according to a spokesman quoted in the Times.
Abedi's father and his younger brother have been arrested by counterterrorist forces, while his elder brother Ismail, 23, was arrested in Manchester following the attack.
Abedi, 22, bought most of the key component parts of the bomb in the days before the attack.
Officers have released the collection of CCTV images - captured at undisclosed locations across the city - in a bid to discover when the terrorist purchased his deadly materials.
The street is linked to Wilmslow Road - the area where investigators said Abedi repeatedly returned in the lead-up to the attack with a blue suitcase they are attempting to recover.
"There has been huge progress made over the week, and the speed of the inquiry remains the same", Jackson said.
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Detectives investigating the Manchester Arena bomber have released more CCTV images of him as they piece together his movements after returning to the United Kingdom from Libya.
"With specialist support we have also have a good understanding of the likely component parts of the bomb and where these came from".
Police have asked for anyone who called them about the bomber before the attack to get in touch.
Police trying to unmask the network behind Abedi searched a property in Wigan, 20 miles (32 kilometers) northwest of Manchester and placed a security cordon around the neighborhood for several hours. "This has led us to the Banff Road area in Rusholme", Jackson said.
Jackson said: "It is vital that we make sure that he is not part of a wider network and we can not rule this out yet".
"We continue to appeal for the public's help in tracking Abedi's movements".
Anyone with information should call the Anti-Terrorist Hotline in confidence on 0800 789321. We need your help as we piece together what happened in the lead up to the attack and if Abedi was helped by anyone.
Meanwhile, Britain's domestic intelligence service MI5 announced it will carry out an internal review of its handling of the Manchester attack, after it emerged Abedi had been known to have extremist views and to be a potential threat. 11 now remain in custody.
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