North Belfast Sinn Féin MLA Gerry Kelly has said loyalist paramilitary gangs should stop making dangerous threats and disband now.
And West Belfast People Before Profit MLA Gerry Carroll has called on the DUP to halt its meetings with those endangering the peace.
It comes after the Loyalist Communities Council (LCC), an umbrella organisation which represents the UVF, the UDA and Red Hand Commando, 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".
Mr Kelly said: “The continuation of threats by loyalist paramilitary gangs, under the umbrella of the Loyalist Communities Council is disgraceful and dangerous.
“Almost 25 years after the signing of the Good Friday Agreement, there is absolutely no place for these armed loyalist gangs in our society.
“Loyalist leaders signed up to the Mitchell Principles of using peaceful and democratic means to settle political differences.
“Yet these groups continue to be involved in murder, intimidation, extortion and drug-dealing and now they are threatening our democracy.
“They should leave the stage and disband.
“Unionist politicians should not be cosying up to people who are making dangerous and violent threats to people and the democratic process.
“The DUP in particular need to show leadership and make it clear that there is absolutely no place for this activity or the continued existence of these criminal loyalist gangs.”
West Belfast People Before Profit MLA Gerry Carroll added: “I would call on the DUP to end all engagements with the LCC.
West Belfast People Before Profit MLA Gerry Carroll
“Representatives of sectarian murder gangs should have no say in politics and the DUP should never have sounded them out on the Protocol.
“We oppose any further concessions on the Protocol, particularly under the threat of loyalist violence.
"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 are only compounding the misery of ordinary people, who are being crushed by the cost-of-living crisis.”
