Speaking from Downing Street after chairing a meeting of the COBRA (Cabinet Office Briefing Rooms) emergency response committee, the British Prime Minister said as many as 1,000 Army troops have already been deployed to boost security operations.
"The police have confirmed that eight suspects remain in custody and that progress is being made in the case but the threat level, as assessed by the independent joint terrorism analysis centre, will remain at critical and the public should remain vigilant," May said in a video message, before leaving for Brussels to attend a NATO summit.
UK officials are said to be "furious" that their investigation was compromised when photos appearing to show debris from Monday's attack appeared in the 'New York Times'.
Greater Manchester Police indicated that information will no longer be shared with US counterparts as the force described the eight men who remain in custody as "significant" arrests in their "fast-moving investigation".
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"As regards the full ongoing investigation, we currently have eight people who have been arrested in connection with Monday's attack. They are all men. A woman who was arrested yesterday has since been released. The arrests have taken place in Manchester, Wigan and Nuneaton. We are now carrying out associated searches at a number of addresses," said Chief Constable Ian Hopkins in a statement.
A further two people were arrested in Libya, taking the total number of people in custody in connection with the bombing worldwide to 10.
Abedi's father, Ramadan Abedi, and brother, Hashim, are the two arrests in Libya. Another brother, 23-year-old Ismail, was arrested soon after the attack and is among the eight men currently in custody in Manchester.
The anti-terror force that took Hashim Abedi into custody in Libya said the teenager had confessed that both he and his brother, Salman, were members of the Islamic State (ISIS) group and that he "knew all the details" of the Manchester attack plot.
Ramadan Abedi fled Tripoli in 1993 after Muammar Gaddafi's security authorities issued an arrest warrant.
He spent 25 years in Britain before returning to Libya in 2011 after Gaddafi was ousted and killed in the country's civil war. He is now a manager of the Central Security force in Tripoli.
Police continue to investigate contacts that suicide bomber Salman Abedi had in the UK and his suspected link to a wider extremist "network".
The channel said its investigation reveals how Abedi grew up on the same housing estates in south Manchester as a group of young men who radicalised each other with some fighting for ISIS in Syria and Iraq.
Information in so-called 'IS Files' -- a huge cache of documents obtained by 'Sky News' - shows how an ISIS fighter called Raphael Hostey, from Moss Side in the south of Manchester, sponsored hundreds of terror recruits.
Abedi and Hostey hung around on the same estates and worshipped in the same Didsbury mosque in Manchester, before they reportedly became disaffected with life in the West.
Abedi had detonated a "nuts-and-bolts" bomb at the end of an Ariana Grande concert as children, teenagers and others were making their way out of Manchester Arena.
Others, including parents, were waiting in the foyer to pick up family and friends when the bomb went off.
Grande has since suspended her remaining Europe-wide tour until June 7.
"We ask at this time that we all continue to support the city of Manchester and all those families affected by this cowardice and senseless act of violence. Our way of life has once again been threatened but we will overcome this together," her management said.
The announcement came as the UK observed a one-minute silence at 11 AM local time today in the memory of all those affected.
Soon after, Queen Elizabeth II arrived at Royal Manchester Children's Hospital to visit the children injured in the attack and the staff at the hospital. Her visit was described as a morale boosting tour for the patients and healthcare professionals caring for them.