Authorities detained a 23-year-old in the southern coastal town of Shoreham-by-Sea, more than 400 kilometers (250 miles) from Manchester. The suspected bomber who also died in the attack is Salman Abedi.
Greater Manchester Chief Constable Ian Hopkins and Deputy Assistant Commissioner Neil Basu, senior national co-ordinator for UK Counter Terrorism Policing, said in a joint statement on Saturday: "In the past five days we have gathered significant information about Abedi, his associates, his finances, the places he had been, how the device was built and the wider conspiracy".
A spokesman said that the brother was aware of Abedi's attack plan and that both men belonged to the Islamic State group, which claimed responsibility for the attack.
The suicide bombing killed 22 people as young as eight and left 59 injured on May 22.
Manchester police yesterday released CCTV footage of 23-year-old Abedi prior to his detonating the bomb that devastated the foyer of the Manchester Arena, and gave details of the bomber's final hours.
Earlier on Monday, police made a 16th arrest as part of the case.
"I believe we can get them to be more successful in working with us to find a way of getting some of that information", she said.
When he was 16 years old, Abedi reportedly travelled during school holidays to fight with his father against the Qaddafi regime in Libya.More news: French president to meet EU's Tusk, reveal minister picks
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Police released photographs from security cameras showing Abedi on the night of the massacre, wearing jeans and trainers, a black body warmer and a baseball cap, with the straps of his backpack visible on his shoulders.
"We should be clear about what this means: A threat level of severe means an attack is highly likely, the country should remain vigilant", Prime Minister May said.
The "We Love Manchester Emergency Fund", launched by the city council and the British Red Cross, had reached £5.65 million by Sunday.
Armed response police stand at the start of the Great Manchester Run in central Manchester, England Sunday May 28 2017.
Abedi was known to United Kingdom security services, but his risk to the public remained "subject to review", according to reports.
May argues that the government has increased funding for security and intelligence agencies.
"But I would not rush to conclusions, as you seem to be, that they have somehow missed something", she said.
The family of one victim, 18-year-old Georgina Callander, said her life had been cut short by "evil, evil men prepared to ruin lives and destroy families".