She also announced in the post that she will be returning to Manchester to hold a benefit concert for the victims of the attack and their families, and that details would come soon.
"The compassion, kindness, love, strength and oneness that you've shown one another this past week is the exact opposite of the heinous intentions it must take to pull off something as evil as what happened Monday", she wrote.
Police have said they have arrested a large part of the network behind the May 22 bombing, which killed 22 people at a concert hall, and two more men were arrested on Saturday as police continued to close in on the group.
On Saturday, Britain lowered its official terrorism threat level from "critical" to "severe" after police said they had dismantled a large part of Abedi's network. Eleven other men between the ages of 18 and 44 also are in custody.
22 persons dead and 59 others injured. Two people were released after questioning without charge, police said. Another brother and Abedi's father have been detained in Libya.
British authorities are racing to round up the terror network behind the Manchester concert bombing after Home Secretary Amber Rudd revealed some of those involved could "potentially" still be at large.
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"We should be clear about what this means: A threat level of severe means an attack is highly likely, the country should remain vigilant", she said. "We won't let hate win".
Police say that 1,000 people are working on the investigation, trying to track down Abedi's accomplices and piece together his movements in the days before he detonated a bomb at an Ariana Grande concert. The Army troops deployed as a result of Operation Temperer will be reduced from Monday night.
From 2009 to 2016, the number of police officers fell by nearly 20,000, or around 14 percent, according to the independent Institute for Fiscal Studies think tank.
A joint statement from Greater Manchester Police Chief Constable Ian Hopkins and Neil Basu, Scotland Yard s senior national co-ordinator from UK Counter Terrorism Policing, added: "This is still a live investigation which is not slowing down".
She refused to say how many times temporary exclusion orders had been used, but confirmed "we have started to use them".
Daesh is another name for ISIS, the terror group that claimed responsibility for the attack.