The petition was launched after last month's murder of 22 year-old Emmett Shiels in the Creggan area of the city and so far, over 600 people have signed it.
However, the bishop declined to add his signature, a decision which was criticised by Mr Shiels's family.
In a statement last week, Dr Hegarty confirmed he had declined to sign the petition and explained his reasons for doing so.
"My call goes to all people who are involved in violence and to any organisation which is associated with violence" he said.
"I would also address myself to groups which accept violence and killing as ever being a legitimate way to progress political aims."
The bishop said that promoting truth and supporting mutual agreement requires very wide and comprehensive understanding.
"That objective has not yet been reached and for that reason the petition seeking support is defective," his statement concluded.
The petition was organised by community workers and calls on the leaders and members of three republican paramilitary groups, the INLA, the Continuity IRA and the Real IRA to abandon their armed campaign and pursue their objectives "through political means only".
It has been signed by several prominent Derry figures including Sinn Féin Deputy First Minister Martin McGuinness, SDLP leader and MP for Foyle Mark Durkan and the former mayor of the city, Drew Thompson, who is a member of the DUP.
The organisers claim that relatives of dead IRA members and of people killed in Derry on Bloody Sunday in 1972 have also added their names to the petition.
The sister of Emmett Shiels, Maureen Wilkinson, who has said she was "disgusted" at Bishop Hegarty's refusal to offer his signature, said the petition was "a positive step in working along with the peace process".
+++++++++++++++++++++++++++++++++++++++++++++++++++
No responsibility or liability shall attach itself to either myself or to the blogspot ‘Clerical Whispers’ for any or all of the articles placed here.
The placing of an article hereupon does not necessarily imply that I agree or accept the contents of the article as being necessarily factual in theology, dogma or otherwise.
Sotto Voce