The University of Salford near Manchester has said in a statement that Abedi had been one of its students - although he reportedly dropped out in recent years - and that it was helping police with their investigation.
She said armed police will also be ready to respond quickly to any incidents and their walking patrols had been increased.
He died at the scene while more than 100 people were injured in the blast.
Addressing the nation from her Downing Street residence, May said armed police who would usually protect strategic points would be replaced by members of the armed forces under Operation Temperer.
"There is damage to major organs, major injuries in terms of limbs and some of these individuals are going to need very long term care and support".
- The explosion took place at Manchester Arena as people began streaming from the doors after a show by USA singer Ariana Grande.
Salman Abedi was born in Manchester to Libyan parents, who reportedly moved to the United Kingdom to escape the Gaddafi regime. Rudd said Britain's operational security could be harmed by the leaks, taking "the element of surprise" away from security services and police.
"The change in the threat level means that there will be additional resources and support made available to the police as they work to keep us all safe".
On Tuesday evening (May 23), The British government, wary of additional possible attacks, raised the national terror threat level to "critical".
Members of the armed forces will be deployed across Britain under police command, and they would be seen at "big events", according to May. Cities including Paris, Nice, Brussels, St Petersburg, Berlin and London have suffered militant attacks in the last two years.
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