The mock bomber dressed in black walked in and shouted at the crowd at Manchester's Trafford Centre overnight as hundreds of people ran screaming and hid in shops and restaurants.
The bomber playing the part of a terrorist repeatedly shouted "Allahu Akbar" (God is great) before acting out the explosion that rocked the food hall, the Independent reported.
Community groups and activists condemned the use of "stereotypes" for the exercise, with some raising concerns it would fuel anti-Muslim prejudice, the paper said.
"The scenario for this exercise is based on a suicide attack by an extremist Daesh (ISIS) style organisation and the scenario writers have centred the circumstances around previous similar attacks of this nature, mirroring details of past events to make the situation as real life as possible for all those involved," he said in a statement.
"However, on reflection we acknowledge that it was unacceptable to use this religious phrase immediately before the mock suicide bombing, which so vocally linked this exercise with Islam.
Dr Erinma Bell, who was made an MBE for her anti-gun campaign work in Manchester, was among those criticising the decision.
"We need to move away from stereotypes if we want to achieve real learning," she wrote on Twitter. "A terrorist can be anyone."
Anti-Islamophobia group the Community Safety Forum called the use of the phrase "Allahu Akbar" offensive and said it was not necessary to make the scenario real, the paper reported.
"This sort of thing panders to stereotypes and further divides us," a spokesperson added. "It will increase anti-Muslim hate crime."
The exercise, codenamed Exercise Winchester Accord, was planned in December and is part of a national programme, coming after previous drills in London, Glasgow and Essex, the paper added.
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