The South Belfast UPRG, an organisation linked to the UDA, is the first group to have broken its silence over recent disorder.
In an appeal to supporters, the group — which has leading loyalist Jackie McDonald as a member — called for an end to violence, saying "street disturbances will not solve our issues".
The unilateral decision by the organisation to speak out came after the Loyalist Communities Council (LCC) failed to reach an agreement on a joint statement condemning the violence.
The Belfast Telegraph understands the umbrella group met on Thursday to discuss the way forward, having been criticised for failing to speak out against a week of disorder.
Members of the LCC are believed to have been split over what their public response to the disorder should be, leading to speculation that the project launched by former Downing Street chief of staff Jonathan Powell in 2005 may be coming to an end.
They are now not expected to make any joint statement condemning the violence, leading to speculation that the project launched by former Downing Street chief of staff Jonathan Powell in 2005 may be coming to an end.
The UPRG said the "recent public disorder has deflected from the original issues that have caused such dismay and anger from within our community".
It added: "The Storey funeral and the subsequent withering report, together with the decision from the PPS to not act against clear law breakers, is as perverse as it is infuriating.
"The Chief Constable has also failed to inspire confidence and his inability to refute the suggestion that a two-tier policing system is operating here in Northern Ireland reduces his role to one of mere appeaser to republican law breaking.
"The ‘protocol’ foisted upon us — without consent nor appropriate justification — has further deeply hurt our community, a community that feels neglected and ignored.
"All of the above issues are political issues that can only be resolved through dialogue and consensus. Rioting, street disturbances and the destruction of property will not change what must be solved by our political representatives.
"We have stated on numerous occasions that the way forward must be through politics alone.
"We implore our supporters, our friends, family members of our friends and anyone with influence to calm tensions, to refrain from posting provocative material on social media and to all come together and galvanise support for our (very well intentioned) concerns and relay this level of concern to our political representatives".
The group also called on unionist politicians "to step forward with clear determination and bring forward proposals that command both support and respect".
"Once again we reiterate — street disturbances will not solve our issues. Politics must be allowed to. We ask for your support during this difficult time," it said.
Infrastructure Minister Nichola Mallon has said bus drivers deserve to be safe following last night's violence in west Belfast which saw a Metro service high jacked and petrol bombed.