The DUP has been urged to end all engagement with a group representing loyalist paramilitaries which appeared to threaten a return to violence.
The Loyalist Communities Council warned of "dire consequences" if Stormont's collapse led to joint authority between the British and Irish governments.
The DUP condemned threats of violence but did not rule out continuing to meet with the LCC, saying it will "engage with people from across loyalism" to "emphasise democratic politics".
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A letter issued by the LCC, an umbrella organisation which represents the UVF, factions of the UDA and Red Hand Commando, said speculation of joint authority had "raised tensions".
The group said activists were "working tirelessly" to "restrain loyalists from lashing out in unproductive ways".
It added: "The message from loyalism should be heard and understood clearly: there are no circumstances in which joint authority would be tolerated, and any effort to impose it would inevitably have dire consequences for the progress made from 1994 onwards."
The letter concluded: "There can be no return to Stormont whilst the Protocol remains in place."
The DUP has been blocking the restoration of the devolved institutions in protest against the post-Brexit trading arrangements, which have angered unionists for creating economic barriers between Northern Ireland and Great Britain.
A 24-week deadline to form a new Executive passed on Friday with the UK Government assuming a legal responsibility to call a fresh election within 12 weeks.
The DUP, which has previously met with the the LCC, was asked if it would continue to engage with the group in the wake of their statement.
A party spokesman said: "Politics and democratic processes are the only way that we will succeed in overcoming the challenges of the Protocol.
"We engage with people from across loyalism and will continue to emphasise democratic politics.
"Violence and/or the threat of it, is never acceptable and the DUP always advocates the democratic route as opposed to arguing that there was 'no alternative' to violence as some have recently said."
Last week after the letter emerged, DUP leader Sir Jeffrey Donaldson said he did not believe there was "any place in our society for threats".
He added: "The last thing we need is more tension, more polarisation, and so I will continue to work and seek to influence others in ensuring what we do is follow the path of politics to get a political solution on the Protocol and on all the other challenges that we face."
People Before Profit West Belfast MLA Gerry Carroll urged the DUP to "end all engagements with LCC".
He said: "The UDA, UVF and Red Hand Commando have nothing to offer working-class communities and should be consigned to the past.
"Violent rhetoric and political brinkmanship over the Protocol is only compounding the misery of ordinary people, who are being crushed by the cost-of-living crisis."
The LCC letter also said the Irish government should not visit Northern Ireland "whilst the Protocol remains, unless and until there is a significant change of attitude and recognition of the legitimate interests of the unionist and loyalist community".
It emerged ahead of claims that a loyalist attack on an Irish government target in the Republic was called off after the Northern Ireland Office last week confirmed there were no plans for joint authority.
The alleged attack was just hours away from being put into action when it was averted, loyalist sources told the Belfast Telegraph.
Earlier this year, Irish government foreign affairs minister Simon Coveney had to leave a peace-building event in Belfast after a hoax bomb alert which was blamed on loyalist paramilitaries.
The PSNI has said it is "aware" of the LCC letter and "will continue to monitor the situation".
It said an "appropriate and proportionate" policing operation is in place for visits to Northern Ireland by Irish government ministers.
In response to the letter, UUP leader Doug Beattie had tweeted: "These loyalist paramilitary groups are bleeding our communities dry with threats of violence and criminal activity. Their control is about money nothing else. If you take direction from them you undermine the Union."
TUV leader Jim Allister said he does not engage with the LCC as it represents proscribed organisations, adding that it was "utterly wrong to be threatening violence".
He told the BBC's Nolan Show that "political action is the way forward and removing the ill-gotten sovereignty of the EU over Northern Ireland is an imperative for all unionists".
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