As runners pounded the streets of the northwestern English city, police arrested a 25-year-old man in the eastern Old Trafford area, bringing the number now detained on UK soil in connection with the attack to 12.
Manchester-born Abedi, a 22-year-old of Libyan origin, killed 22 people on Monday evening when he targeted a pop concert by US teen idol Ariana Grande. A third of the those slaughtered were children and another 116 people were injured.
Asked by the BBC if some of Abedi's network were still at large, British Home Secretary Amber Rudd said: "Potentially."
"The operation is still really at full-tilt in a way and so until the operation is complete we can't be entirely sure that it's closed."
Authorities in Libya have detained Abedi's brother and father, while British investigators appealed to the public late Saturday for details of the bomber's movements in the days before the attack, which has been claimed by the Islamic State group.
Police released photographs from security cameras showing Abedi on the night of the massacre, wearing jeans and trainers, a black bodywarmer and a baseball cap, with the straps of his backpack visible on his shoulders.
The police statement said one of the last places he went to was a "city centre flat and from there he left to make his way to the Manchester Arena" where the attack took place.
"The flat is highly relevant as a location which we believe may be the final assembly place for the device."
- 'Don't let them win' -
Security was highly-visible as 40,000 runners took to Manchester's streets for the Great Manchester Run a day after Prime Minister Theresa May lowered the terror threat level, which was hiked following Monday's carnage.
Competitors gathered at the start line and fell silent as the clocks struck 9:00 am (0800 GMT). This was followed by sustained applause as the song "Don't Look Back In Anger" by Manchester band Oasis was played over the tannoy, sparking a sing-a-long.
"After everything that's happened in Manchester, to get everyone to come together, stand united, don't let them win, that's why I'm doing it," runner Ian McLellan, 45, told AFP.
British counter-terror chief Mark Rowley said Friday that police had captured "a large part of the network" linked to the bombing.
Investigators say they have a 1,000-strong team working "around the clock" on the probe and have significant details on Abedi's associates and movements, his finances, and how the explosive was built.
Britain on Saturday reduced its terror threat level from critical -- its highest level -- to severe.
Operation Temperer, which involved the deployment of troops on patrol alongside police, will be wound down on Monday night, at the end of the bank holiday weekend.
"From midnight on Monday, there will be a well-planned and gradual withdrawal of members of the armed forces, who will return to normal duties," the premier said.
- 23,000 on UK terror radar -
May has seen her polling lead against the Labour party's Jeremy Corbyn dwindle as campaigning restarted ahead of a June 8 general election, with her rival accusing her of overseeing a cut in police staff while she was interior minister.
From 2009 to 2016, the number of police officers fell by almost 20,000, or around 14 percent, according to the independent Institute for Fiscal Studies think tank.
May argues that the government has increased funding for security and intelligence agencies.
Authorities are currently handling 500 terror-related investigations into 3,000 individuals, with another 20,000 people on the radar posing a "residual risk".
May attempted to hit back late Saturday, announcing the new "Commission for Countering Extremism" and saying that "enough is enough -- we need to be stronger and more resolute in standing up to these people".
The commission will have a legal responsibility to identify extremism and will advise the government about what policies and laws to enact in order to defeat extremists.
The family of Georgina Bethany Callander, an 18-year-old killed in the bombing, released a tribute late Saturday in which they called on the government to "open its eyes" to prevent further tragedy.
"I wish I could say that Georgina is one of the last to die in this way but unless our government opens its eyes we know we are only another in a long line of parents on a list that continues to grow," said the family in a statement.
The bombing was the latest in a series of IS-claimed attacks in Europe that have coincided with a US-led offensive against the jihadist group in Syria and Iraq.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)