The U.K.'s terror threat level has been classed as severe since August 2014.
The suspected attacker, Abedi, has not yet been formally identified by the coroner, Manchester police said. As part of the security response, military personnel are being deployed into civilian areas to work alongside and bolster police.
The father of the 22-year-old Briton who police say bombed a concert in Manchester was detained for interrogations Wednesday in the city of Tripoli.
Rudd said up to 3,800 soldiers could be deployed on Britain's streets, taking on guard duties to free police to focus on patrols and investigation.
Prime Minister Theresa May said the blast was timed to "cause maximum carnage" and targeted "the young people of our society with cold calculation".
The threat level was raised this high only once prior, in 2006, in an effort to foil an Al-Qaeda plot to use liquid explosives on transatlantic flights.
Earlier attacks, including vehicle-borne assaults in Berlin and Stockholm, have coincided with an offensive on IS redoubts in Syria and Iraq by US, British and other Western forces.
Witnesses described the horror when the bomber blew himself up.
All three were injured, the husband critically, the corporation said.
Manchester attacker's younger brother arrested in Tripoli: spokesman
The elder Abedi told the Associated Press by telephone from the Libyan capital of Tripoli: "We don't believe in killing innocents. It brings to four the total number of people who are being questioned by police after a 23-year-old male was detained yesterday.
One of the five was carrying a package when he was arrested in the town of Wigan, 17 miles (27 km) to the west of Manchester city center, police said.
Police promised extra measures at showpiece events coming up such as Saturday's FA Cup football final. Britain also has a national election scheduled for June 8.
Thousands have taken part in a vigil in the northern United Kingdom city's centre.
Singaporeans in Manchester are in a state of shock after Monday's terror attack.
US President Donald Trump and European leaders issued vows of defiance.
Meanwhile, eight of the 22 victims of the attack are known to be eight-year-old Saffie Roussos, Lisa Lees, 50- year-old Jane Tweddle-Taylor, 29-year-old Martyn Hett, 15- year-old Olivia Campbell, 32-year-old Kelly Brewster, 28- year-old John Atkinson, and 18-year-old Georgina Callander.
Sixty-four people are still hospitalized, Jon Rouse of the Greater Manchester Health and Social Care Partnership said Wednesday.
He was believed to have come through unsecured outer doors with parents waiting to pick up their children.
"The intelligence services know a lot of people, and I'm sure we will find out more what level they knew about him in due course", she told the BBC.
"All acts of terrorism are cowardly attacks on innocent people, but this attack stands out for its appalling, sickening cowardice, deliberately targeting innocent, defenseless children and young people who should have been enjoying one of the most memorable nights of their lives", she said.
"We ran and people were screaming around us and pushing on the stairs to go outside and people were falling down, girls were crying, and we saw these women being treated by paramedics having open wounds on their legs.it was just chaos", said Sebastian Diaz, 19.