In video footage of the exercise broadcast on British television, a masked man dressed in black could be seen running into the complex in Manchester shouting the words before setting off a bomb and falling to the floor.
"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," said Garry Shewan, a senior officer at Greater Manchester Police.
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In a statement, Shewan said the scenario had been based on "a suicide attack by an extremist Daesh-style organisation" -- Daesh being an Arabic acronym for the Islamic State group -- but added: "We recognise and apologise for the offence that this has caused."
The phrase is Arabic for "God is greatest."
Tony Lloyd, mayor of Greater Manchester, said using the phrase was "ill-judged, unnecessary and unacceptable".
"It didn't add anything to the event, but has the potential to undermine the great community relations we have in Greater Manchester," he said.
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The role play exercise on the outskirts of Manchester involved 800 people, including actors made up to resemble gunshot victims with horrific injuries.
Police said there was no specific threat in Manchester and that the exercise was devised in December a month after the Paris attacks which killed 130 people and were claimed by Islamic State jihadists.
Britain's terror threat level remains at severe, which means the security services consider an attack to be "highly likely".
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