The centre, based in the south of the city, issued a short statement at about 7.30am on Tuesday saying its members were “shocked and horrified” .
It also re-posted a message from the Muslim Council of Britain which said: “May the perpetrators face the full weight of justice both in this life and the next.”
The statements were posted on Facebook, and following a string of comments from other web users the Islamic Centre then added: “I assure you the Muslim community are just as heartbroken this morning as everyone else.
“While we don’t know yet who did it, terror groups do not work like the terrorist groups did here.
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“There is no common cause, no sense of support, only bewilderment at how someone can kill innocent people.
“They work in cult-like secrecy, often via the internet, few of us will ever meet anyone with these sort of sympathies.”
It added some terror attacks have been thwarted by Muslims reporting threats to police.
“Extremists don’t view us ‘mainstream’ Muslims as Muslim either, which is why they have killed so many Muslims worldwide,” it said.
“They are a law unto themselves.”