ISIS said one of its "soldiers" managed to place explosive devices at the concert - a version that was at odds with the police assertion that the attack was carried out by a lone suicide bomber carrying a homemade device.
The blast marked the deadliest terror attack on British soil since the 2005 London bombings.
"We believe at this stage the attack last night was conducted by one man", said Greater Manchester Police Chief Constable Ian Hopkins at a televised news conference.
While claiming responsibility on its Telegram account, the group appeared to contradict the police description of a suicide bomber.
Also on Tuesday, police arrested a 23-year-old man outside a nearby supermarket.
Numerous blast victims were children or teenagers who had attended a concert by American singer Ariana Grande at the Manchester Arena, which was packed to its capacity of 21,000. The police raided the house on Tuesday afternoon, after setting off a controlled explosion to gain entry.
Home Secretary Amber Rudd decried "a barbaric attack, deliberately targeting some of the most vulnerable in our society - young people and children out at a pop concert".
President Trump, in Bethlehem, said the attack preyed upon children and described those responsible as "evil losers". Afterward, the man, identified as Andy, said he saw about 30 people "scattered everywhere".
"It is a possibility that we can not ignore that there is a wider group of individuals linked to this attack", she explained, adding that soldiers will be deployed to help local police protect city streets nationwide. "Not let them stop us going about our daily business and create fear and we must all live in harmony with each other as we stand together and defeat terrorism".
One of the youngest victims was named on Tuesday as Saffie Rose Roussos from Leyland, near Preston.
Chris Upton, the head teacher at the Tarleton Community Primary School, described her as "simply a lovely little girl" who was "quiet and unassuming with a creative flair". "Just lovely to speak to", said Peter Rawlinson, deputy of the Bishop Rawstorne Church of England Academy in Croston. Officials said several school-age children were among them.
Grande, who had just finished the first of three scheduled United Kingdom performances, tweeted about her devastation several hours later: "broken. from the bottom of my heart, i am so so sorry. i don't have words".
The pop star has suspended her "Dangerous Woman" tour following the attack, a source with knowledge of the situation told CNN.
Queen Elizabeth released a statement on the incident, noting the nation's shock at the bombing.
"Critical" is the top level of Britain's terror threat system.
Police have been warning that another attack was highly likely after a man plowed his vehicle into a crowd on London's Westminister Bridge in March and stabbed a policeman, in an attack that left six dead.
"These were children, young people, and their families. This was an evil act".
Abedi was killed at the scene of the attack, though authorities have yet to confirm whether he was part of a larger network. Security has also been boosted in London.
"I do not want to unduly alarm the members of the public", May said from Downing Street.
"Precisely how the military and armed police officers will be deployed is an operational decision for police commanders, and Assistant Commissioner Mark Rowley of the Metropolitan Police will be making a statement giving further details from Scotland Yard later this evening".
Charlotte Campbell told the BBC on Tuesday morning that she's "phoning everybody", including hospitals and centers trying to locate her 15-year-old daughter Olivia.
Outside, she said, "you could smell the burning". Her father is now looking for the girls.