They spoke out after suicide bomber Salman Ramadan Abedi detonated an explosive device outside the Manchester Arena on Monday night. Sheffield woman Kelly Brewster is reportedly among the dead.
Members of the Ahmadiyya Muslim Community UK group in Sheffield attended vigils for the victims in both Sheffield and Manchester last night.
Saleem Ahmad, president of the group, said: "Never can such attacks be justified in any shape or form and so all forms of terrorism and extremism must be condemned in the strongest possible terms.
"May God comfort the bereaved and those affected in any way."
Shahid Ali, a presenter at Sheffield-based community radio station Link FM, said: "As a parent I look on this cowardly, horrific and barbaric act with horror and cannot imagine the pain of those parents and families grieving. It was brought home to me when a friend's daughter attended the concert but was thankfully safe and unhurt.
"We must not allow these murderers and thugs to succeed by furthering mistrust and division. Instead we must promote our far superior, positive message.
"The extremists want to ensure our communities turn on one another. We must take the poison out of their message by showing how we come together to aid and support one another as one community."
He added: "I was heartened yesterday as I travelled around Sheffield that people who, normally wouldn't give you a second glance as they get on with their everyday routines, went out of their way to catch my eye and give me a small welcoming smile.
"This has made me proud to be a son of Sheffield. We can defeat this extremism, but only by playing our smaller part in the bigger picture."