Ten men are now in custody in connection with the attack that killed 22 people.
The British-born 22-year-old of Libyan descent detonated the blast on Monday evening, killing 22 people outside a packed Manchester Arena after a show by US pop star Ariana Grande.
British interior minister Amber Rudd on Wednesday described the bombing as "more sophisticated than some of the attacks we've seen before", adding that "it seems likely -- possible -- that he wasn't doing this on his own".
Ten men are now in custody in connection with the attack, including Abedi's brother and father in Libya.
Abedi reportedly returned from Libya only a few days before the bombing and police are still trying to pin down his movements and determine whether he was part of a wider network.
Police have revealed little about the explosive. But photographs from the bomb scene leaked to The New York Times -- to the fury of British officials -- suggest Abedi carried "an improvised device made with forethought and care", the newspaper wrote.
The images showed shreds of a blue Karrimor backpack, metal screws and nuts, the remains of a powerful battery, and an apparent hand-held detonator.
While some parts of the device would be easy to acquire, "the detonator itself is not something that's easy to get your hands on without raising suspicions," British security expert Will Geddes told AFP.
"Putting together devices of this nature is not an easy job," said Geddes, who heads the corporate security ICP Group.
"Rarely is there going to be a lone actor with IEDs (improvised explosive devices) -- there are lots of individuals, lots of moving parts."
Britain's The Times newspaper on Friday said Abedi was believed to have planned the attack for at least a year, buying nails and screws for the device from hardware stores in the northwestern English city before his Libya trip.
Security sources fear he may have also made a second device which is now in the hands of other jihadists, The Daily Telegraph newspaper reported.
"This is not a lone-wolf case involving a knife," said Republican lawmaker Michael McCaul, who chairs the US House committee on homeland security.
McCaul told Fox News television that Monday's bombing was "a very soft target, a very premeditated sophisticated attack using a very sophisticated explosive device".
After his return from Libya, Abedi was seen on security cameras last Friday buying the Karrimor rucksack at a Manchester shopping centre, after which he is thought to have assembled the device at two different addresses, the Telegraph said.
"He will have spent time at a camp somewhere, possibly in Libya, being shown how to do it," former Metropolitan police officer David Videcette, who helped investigate the 2005 London bombings, told the broadsheet.
The New York Times said there were no initial details of the type and strength of the explosive used in the attack.
But details including the location of the bodies of those struck by the bomb, and the remains of the bomber himself, "are indicators of a powerful, high-velocity charge, and of a bomb in which its shrapnel was carefully and evenly packed," the daily said.