The Northern Ireland secretary's department has said democracy rather than violence is the way to express frustrations as it responded to concerns over a group representing loyalist paramilitaries.
It follows the Loyalist Communities Council warning of "dire consequences" if Stormont's collapse led to joint authority between the British and Irish governments.
In a letter the umbrella organisation, which represents the UVF, factions of the UDA and Red Hand Commando, said activists were "working tirelessly" to "restrain loyalists from lashing out in unproductive ways".
Read more: DUP leader's claim that Brexit Protocol 'delayed heart surgery' dismissed by Belfast Trust
The warnings of violence were roundly condemned by Stormont parties.
It emerged ahead of claims that a loyalist attack on an Irish government target was called off after the Northern Ireland Office confirmed there were no plans for joint authority.
The NIO was asked about the LCC letter and reports from loyalist sources to the Belfast Telegraph about the alleged attack.
The UK Government department, whose representatives have previously met with the LCC, did not say whether it would continue to engage with the loyalist group.
But in a statement, an NIO spokesman told Belfast Live: "We have been clear. Joint authority is not being considered.
"The UK Government is absolutely clear that the consent principle governs the constitutional position of Northern Ireland. We will not countenance any arrangements that are inconsistent with that principle."
He added: "We do not comment on security matters. Individuals involved in this sort of activity are not supported by local communities or wider society.
"The right way to express concerns or frustrations is through dialogue, engagement, and the democratic process, not through violence."
It comes after the DUP was urged to end all engagement with the LCC following its letter, which had also called for Brexit's Northern Ireland Protocol to be scrapped.
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".
Sir Jeffrey Donaldson's party has been blocking the restoration of the devolved institutions in protest against the protocol, which has angered unionists for creating trade 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.
Secretary of State Chris Heaton-Harris is to hold further talks with Stormont party leaders on Tuesday.
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.
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