The Muslim Council of Britain, which sent a delegation to Iraq last month to try and win Mr Bigley's release, said: "We are appalled and profoundly saddened by the cold-blooded murder of Kenneth Bigley after a protracted period of mental torture and anguish.
"We offer our heartfelt sympathy and condolences to the family who have gone through the most dreadful experiences."
The council's general secretary, Mr Iqbal Sacranie, said the action was "completely and utterly rejected" by the vast majority of the Muslim community.
The Islamic Human Rights Commission added: "We send our deepest condolences to Mr Bigley's family, as we do to the families of all those killed in Iraq as a result of the war and occupation."
Meanwhile, Mr Akbar Ali, a Muslim leader in Liverpool, said: "We are very sad, we were all hoping he would be reprieved and representations had been made.
"This group are very, very ruthless people without aims or objectives, just trying to show the world how cruel and mindless they can be. They are giving a very, very negative picture of Islam."
Mr Ali said that he did not fear a backlash against the Muslim population despite the fate of Mr Bigley.
"That little bit of shadow is always there but we have been working together, so there are no immediate fears." - (PA)