29 May, 2017
Police have said they have arrested a large part of the network behind the bombing, which killed 22 people at a concert hall, and two more men were arrested on Saturday as police continued to close in on the group.
Armed police guard the area during the Great Manchester Run in Manchester, England Sunday, May 28, 2017.
"Until the operation is complete, we can't be entirely sure that it is closed", Rudd said. Investigators say they have dismantled a large part of his network, but expect to make more arrests.
The investigation into Abedi, who was known to security agencies and had just returned from Libya before the bombing, has so far led to the detention of 12 people.
Police have released surveillance-camera images of Abedi on the night of the attack that show him dressed in sneakers, jeans, a dark jacket and a baseball cap. The straps of a knapsack are visible on his shoulders.
Authorities are appealing for more information about his final days.
Prime Minister Theresa May said developments in the investigation into the bombing meant intelligence experts had made a decision to lower the threat level from its highest rating "critical", meaning an attack could be imminent, to "severe".
Peter Hook, a member of seminal Manchester band New Order, was among the runners and said the tragedy had brought people together.
Abedi was known to United Kingdom security services, but his risk to the public remained "subject to review", according to reports.
Abedi had been a former "subject of interest" to MI5, but Ms Rudd said: "The intelligence services are still collecting information about him and about the people around him".
"We will continue in honour of the ones we lost, their loved ones, my fans and all affected by this tragedy", she added, before ending by saying those that lost their lives will always be in her thoughts: "They will be on my mind and in my heart everyday and I will think of them with everything I do for the rest of my life".
"I would not rush to conclusions. that they have somehow missed something", Rudd said.
Police said they are working "around-the-clock" with more than 1,000 people involved in the investigation, pursuing more than 1,500 "actions". Eleven other men, aged between 18 and 44, are in custody.
"Officers have also arrested a 25-year-old man in the Old Trafford area on suspicion of offences contrary to the terrorism act", the spokesperson said.