Amber Rudd said "potentially" other members of Abedi's group could still be out there and "we can't be entirely sure that it is closed".
"The public should be clear about what this means".
Britain's terror threat level was yesterday reduced to "severe" from "critical". "The country should remain vigilant".
The images are the first to show how the 22-year-old looked when he detonated the bomb he was carrying in the worst terror attack in Britain for more than a decade.More news: LeBron James breaks Michael Jordan's playoff scoring record
"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. Police say that 1,000 people are working on the investigation, trying to track down bomber Salman Abedi's accomplices and piece together his movements in the days before the attack.
Security services had feared an experienced bomb-maker could be large but a source with knowledge of the investigation told Reuters on Thursday Abedi might have made the bomb himself or with an accomplice, lessening the risk of another attack.
Rudd said Britain was making good progress with the Internet companies on this but that more could be done. "There is still much more to do".
"There will be more arrests and there will be more searches", he said.
Mr Rowley admitted there were still "gaps in our understanding" of 22-year-old Abedi's network and said it will "take a little more time" to close them.More news: Errol Spence Jr. Beats Kell Brook via TKO in 11th Round
Armed police were on the streets outside London's Wembley Stadium, and security guards conducted extra bag checks, as 90,000 fans arrived for the FA Cup soccer final between Chelsea and Arsenal, one of the biggest sporting events of the year.
Despite the alert, police have urged people to go out and enjoy themselves over the three-day holiday weekend.
"Whilst we can't directly link these to the events of Monday night, we're continuing to monitor the situation and support our communities".
Political campaigning for the June 8 national election which was suspended after the Manchester attack resumed on Friday with the bombing becoming a central feature.
British Prime Minister Theresa May said "a significant amount of police activity" and several arrests had led to the level being lowered.More news: South Korea OKs civilian contact with North Korea over malaria
She said: "There is nothing I or anyone can do to take away the pain you are feeling or to make this better".