A UDA statement calling on loyalists to "be ready for battle" has been attacked by the SDLP, Sinn Féin and Alliance Party.
However, it has been defended by the Ulster Political Research Group (UPRG), which is linked to the paramilitary organisation.
The group denies the UDA statement was a call to arms.
In a statement issued to coincide with the 90th anniversary of the ending of the first World War, the UDA accused republicans of "racism, ignorance and bigotry" and of "challenging our very existence at every level".
It said: "We need more of our members to participate in the challenges that lie ahead. They must understand that the threat from Irish republicanism and nationalism has not abated: they are challenging our very existence at every level.
"They are challenging through agitation and non-violence but it is every bit as dangerous and must be combated."
The statement continued: "Our message to Irish republicanism and Irish nationalism is very simple - they must understand we have our own distinct identity and that we are British, and it is us who will define who we are, the same as we have come to understand that Irish republicans/nationalists must determine their own identity/nationality."
Republicans should follow their own creed, the statement added, "and recognise the identity and national self-determination of the British people in Ulster".
Referring to this month's homecoming parade by British army soldiers, sailors and airmen at which there was a republican protest, the UDA was scathing. Accusing republicans of "racism, ignorance and bigotry", the loyalist organisation said: "They squandered a massive opportunity to reach out to unionism in a bid to understand us as a people and as human beings whose only crime is that we are different to them."
Sinn Féin Assembly member Jennifer McCann said there was concern as to what the UDA statement actually meant, while SDLP Assembly member John Dallat said the "belligerent bluster" from the loyalists could not go unchallenged. He also accused First Minister Peter Robinson and Deputy First Minister Martin McGuinness of a failure of leadership.
Dr Stephen Farry of the Alliance Party said: "It is hard to conceive of a less appropriate organisation than the UDA to campaign on behalf of British values."
However, Frankie Gallagher of the UPRG said there was no threat of violence in the UDA statement.
He said the UDA was calling on loyalists "to do battle in terms of social economy, in terms of bringing jobs into Protestant communities, in terms of unionist unity".