The prime minister said Tuesday that the death toll from the attack stood at 22 and "59 people remain injured - and many of them have life-threatening conditions".
Home Secretary Amber Rudd earlier told the BBC that Abedi was on the radar of intelligence services.
Severe is level 4 out of 5, with critical being the highest.
"This means that their assessment is not only that an attack remains highly likely but that a further attack may be imminent", May said in a televised statement from her Downing Street Office after a meeting of the government's crisis response committee.
May said that "armed police officers responsible for duties such as guarding key sights, will be replaced by members of the armed forces, which will allow the police to significantly increase the number of armed officers on patrol in key locations".
"You might also see military personnel deployed at certain events such as concerts and sports matches, helping the police to keep the public safe".
He had recently returned from Libya and France's interior minister said he had probably travelled to Syria at some point.
Greater Manchester Police said they were called to the Manchester Arena just before 10:35 p.m. local time on Monday.
Asked whether the US leaks had compromised the investigation, she said: "I wouldn't go that far but I can say that they are perfectly clear about the situation and that it shouldn't happen again". They're losers and we'll have more of them. "And as I say, we will find out more when the operation is complete", she said.
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President Donald Trump has been more sympathetic to Israel's settlement policies than the fiercely critical Obama administration. Ambassador to the United Nations , put it, both the Israelis and Palestinians want to give the new administration a chance.
The blast marked the deadliest terror attack on British soil since the 2005 London bombings. But it will have reverberations far beyond British shores.
Attacks in cities including Paris, Nice, Brussels, St Petersburg, Berlin and London have shocked Europeans already anxious over security challenges from mass immigration and pockets of domestic radicalism.
The militia claims that the younger Abedi admitted knowledge about the Manchester attack and was in Britain for its planning. Abedi died in what appears to have been a suicide bombing. It suggested explosive devices were placed "in the midst of the gatherings of the Crusaders". That reference, however, was later removed. Queen Elizabeth II described bombing as "act of barbarity". The election campaign has been suspended for now as a mark of respect.
Georgina Callander, 18, was also killed, according to her school, the Bishop Rawstorne Church of England Academy.
The U.N. Security Council condemned "the barbaric and cowardly terrorist attack" and expressed solidarity with Britain in the fight against terrorism. United Kingdom to hold minute of silence Thursday morning. Police have carried out two raids in Manchester.
On Tuesday evening, hundreds attended a vigil outside Manchester City Hall in honor of the victims.
The mayors of several major cities across the globe, including those of London and New York City, also said they were reviewing their security measures as a precaution after the attack.
Twenty-two people were killed, including children, and dozens were wounded in the attack claimed by Islamic State.