The Most Reverend Donal McKeown was speaking in the wake of a double shooting in the city on Saturday evening.
Police said a 48-year-old man was shot in his thigh and shin and a 31-year-old was shot in his thigh.
One of them men is in the intensive care unit at the Royal Victoria Hospital in Belfast in a critical condition.
The second man has been discharged from hospital.
“This is an awful incident, a man’s life has been seriously endangered, and the message goes out violence is the way to solve problems,” Bishop McKeown told BBC Radio Foyle.
“This community has decided this is not the way forward, it doesn’t want this in its name. Whatever problems may be arising, violence is not a solution to any of them”.
Police said they believe violent dissident republicans carried out the two shootings in Creggan’s Rinmore Drive around 6.35 pm on Saturday, February 6.
A senior detective investigating the double gun attack said it was the fourth shooting in Derry so far in 2021.
Bishop McKeown added: “Ultimately it’s the challenge for politicians and for the policing board to ensure this community, where these shootings took place, can have visible, accessible and responsive policing.
“It is when there is a gap, an absence of that on the ground, other people will want to fill the gap to claim some kind of credit or leadership in the community for themselves, brutal though their actions may be.”
He said there is an onus on “everyone in a leadership position, in church, in state and in communities, to ensure they build hope at a time like this that things can be better”.
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