Salman Abedi killed 22 and injured 64 when he blew himself up at the Manchester Arena on Monday night - 20 people are in critical care.
Police arrested three men in south Manchester on Wednesday.
The UK terror threat level is now up to its highest level of "critical", meaning more attacks may be imminent.
It means military personnel will now be deployed to protect key sites.
Mrs Rudd said the attack was a "devastating occasion".
"It was more sophisticated than some of the attacks we've seen before, and it seems likely - possible - that he wasn't doing this on his own," she added.
Five of the victims are known to be eight-year-old Saffie Roussos, Olivia Campbell, 15, Kelly Brewster, 32, John Atkinson, 28, and Georgina Callander - thought to be 18.
Two Polish people are also among those killed, according to a Polish government minister.
The injured are being treated at eight Greater Manchester hospitals. Of those, some have lost limbs.
The wounded include 12 children aged under 16.
Several people are still missing, including Eilidh MacLeod, 14, from Barra in the Outer Hebrides, Chloe Rutherford, 17, and Liam Curry, 19.
Eilidh's friend, Laura MacIntyre, 15 - who was also reported as missing - was later identified as one of the seriously injured in a Manchester hospital.
Manchester metro mayor Andy Burnham told the BBC that the attack had been the city's "darkest hour".
A hotline has been set up for people concerned about loved ones - 0800 096 0095.
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