Police officers guard the entrance to a street in the Moss Side area of Manchester on May 28, 2017 during an operation.
Interior Minister Amber Rudd told Sky News that this was a "right first step" for MI5 to take in the wake of the bombing that killed 22 people at a pop concert by US singer Ariana Grande.
CCTV stills of Abedi, bespectacled and casually clothed, were released by police in a plea for information about his movements between May 18 and the attack.
Britain said on Monday intelligence service MI5 was reviewing its processes following a suicide bomb attack which killed 22 people in Manchester, as questions continue over how much the authorities knew about the assailant.
Greater Manchester Police said a 25-year-old man was arrested in the city on suspicion of terrorist offenses.
A woman and a 16-year-old boy had been released without charge, leaving 13 men still in police custody in relation to the attack, including four who had been charged with terrorism or firearms offences. Most of the searches and arrests since Monday night's bombing have been in multi-ethnic south Manchester, where Abedi - the son of Libyan parents - was born and raised. A third of the those slaughtered were children and another 116 people were injured.
Abedi died in the blast.
Police said their investigation is "making good progress" and has around 1,000 people working on it.
Asked by the BBC if some of Abedi's network were still at large, British home secretary Amber Rudd said, "Potentially".
"Until the operation is complete, we can't be entirely sure that it is closed". Abedi was listed at the property along with his older brother, Ismail.
The images show Abedi in the hours before the attack, wearing sneakers, jeans, a dark jacket and a baseball cap. The straps of a backpack are visible on his shoulders.
Authorities detained a 23-year-old in the southern coastal town of Shoreham-by-Sea, more than 400 kilometers (250 miles) from Manchester.
MI5 has launched a "post incident investigation" into how the Manchester bomber was overlooked, while a separate report is being prepared for ministers and those who oversee the work of the service. In Rome, Pope Francis led thousands of people in St. Peter's Square in prayer, saying he was "close to the relatives and all those who are weeping for the dead".
Security remained high at major events across Britain on Sunday, including the Great Manchester Run road race, where police armed with submachine guns protected participants and spectators.
Peter Hook, a member of seminal Manchester band New Order, was among the runners and said the tragedy had brought people together. "They picked the wrong people to mess with this time".
Abedi was known to United Kingdom security services, but his risk to the public remained "subject to review", according to reports.
When asked how many potential militants the government was anxious about, Rudd said the security services were looking at 500 different potential plots, involving 3,000 people as a "top list", with a further 20,000 beneath that.
"But I would not rush to conclusions, as you seem to be, that they have somehow missed something", she said.