In an interview with The Times last weekend, Atkinson said Bulger's killers Jon Venables and Robert Thompson "shouldn't have been tried in an adult court because they were still children".
She added: "In most Western European nations they have a completely different way of intervening with youngsters who've committed crime. Most of their approaches are more therapeutic, more family and community-based, more about reparation than simply locking somebody up."
Responding to Atkinson's comments, Bulger's mother Denise Fergus said: "This woman owes James and me an apology for her twisted and insensitive comments. Then she should resign, or be sacked."
But following publication of The Times interview, Atkinson issued a statement that said she wished to "be clear and put into context my views on such terrible atrocities".
"Some children and young people do commit terrible crimes and are a danger to themselves and to others," the statement said.
"It is right therefore that these children are contained in secure settings as in the case of James Bulger's killers and, more recently, the horrific case in Edlington."
The statement added that Atkinson empathised with the pain of victims' families and that children responsible for such atrocities "need to understand the severity of their actions".
Atkinson said perpetrators should undertake intense programmes — appropriate to their age — in secure facilities where they are helped to make "positive and lasting changes" to their behaviour.
She added: "The age of criminal responsibility in England is one of the lowest in Europe. The statistics show that we are in danger of criminalising too many children and young people by locking them up for committing far less serious crimes."
