A 23-year-old man was arrested on Tuesday in the wake of the attack on Monday night, carried out by a bomber identified as 22-year-old Libyan-origin Salman Abedi. The BBC has reported that the man arrested on Tuesday is Abedi's brother Ismail.
"Three men have been arrested after police executed warrants in South Manchester in connection with the ongoing investigation into Monday night's horrific attack at the Manchester Arena," a Greater Manchester Police statement said.
UK Home Secretary Amber Rudd said on Tuesday that Abedi was known to security services "to a point" and it is believed intelligence agencies had dug into his connections with the Al Qaeda and Islamic State (ISIS) in his parents' homeland of Libya.
Manchester-born Abedi went to school locally and then studied business management at Salford University, before dropping out from the course.
He made several trips to Libya, where it is thought his immigrant parents had returned in 2011 following Muammar Gaddafi's overthrow.
Mohammed Saeed El-Saeiti, the imam at the Didsbury mosque where Abedi's brother Ismail had been a Quran teacher, branded the attacker as someone filled with hate.
"Salman showed me the face of hate after my speech on ISIS," he said.
Meanwhile, eight-year-old Saffie Roussos, 15-year-old Olivia Campbell, 28-year-old John Atkinson, 18-year-old Georgina Callander and 32-year-old Kelly Brewster are among the first of the 22 victims of the attack to be named.
Two Polish parents were also killed while collecting their daughters from the venue, the Polish Ministry of Foreign Affairs has said.
Foreign Minister Witold Waszczykowski told a Polish radio station: "The parents came after the concert to collect their daughters and unfortunately we have information that they are dead. The children are safe."
The Polish Foreign Ministry, which did not name the couple, said: "We share the pain of the family and the loved ones of the victims and express our most sincere condolences."
A vigil was held in Manchester's Albert Square on Tuesday evening as a show of support for victims and their families.
Greater Manchester Police has asked people to remain vigilant and report anything suspicious to the Anti-Terrorist Helpline.
Deputy Chief Constable Ian Pilling said British Prime Minister Theresa May's announcement of raising the threat level to its highest at "critical" will provide the force with additional resources to conduct their investigations.
"We are continuing to work with the national counter-terrorism policing network and UK intelligence services as part of the response to dealing with the tragic events," he said.
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