May said members of the armed forces would be positioned at key sites to free up police for patrols and military personnel might be deployed at public events.
The men were arrested in southern Manchester, local police said, a day after an unnamed 23-year-old was collared in connection with the blast.
Abedi went to school in Manchester and on to Salford University before dropping out, and worked in a bakery.
"A huge bomb-like bang went off that hugely panicked everyone and we were all trying to flee the arena, " said 22-year-old concertgoer Majid Khan.
A sign is seen in central Manchester.
She said security services were working to see if a wider group was involved in the attack, which fell less than three weeks before a national election.
Counter-terrorism agencies have mounted a massive inquiry into the outrage, which was the worst terrorist attack since 52 innocent people were killed in the 7 July bombings in London in 2005.
Violence has once again struck music fans with a suicide attack on Ariana Grande's Manchester show, but the booming concert industry hopes to withstand the new shock.
"This is the world we have been living in for a few years", he said.
Best known for her singles "Problem" and "Break Free", Grande is credited with having an exceptionally broad vocal range for a pop star.
The city's regional government and its mayor, Andy Burnham, were among scores of Twitter users who circulated the MissinginManchester hashtag, used by people looking for family members and friends. Twelve of them were aged under 16.
"From the bottom of my heart, I am so so sorry".
In the city centre, thousands gathered for a multi-faith vigil outside the Town Hall to remember the victims, with defiant chants of "Manchester!"
"In modern Britain everyone seems petrified to officially say what we all say in private".
Law enforcement in the United Kingdom continued to expand its investigation Wednesday, citing a wider terror network and arresting at least six people in connection with the attack.
There was a terror attempt on parliament in March.
Queen Elizabeth II condemned the Manchester attack as an "act of barbarity" and observed a minute's silence at a Buckingham Palace garden reception.
Additionally, the reaction of most people in the aftermath of the attack has been positive - Sikh, Muslim and other communities all banded together in condemning the unjustified tragedy, and offered help in whatever way possible - taxi owners provided free transport to hospitals while residents of the area offered rooms in their houses to use if needed.