DUP leader and First Minister Arlene Foster said she has been made aware of a threat against her by the South East Antrim UDA.
Mrs Foster said she understands the threat was issued because of her support for the family of murder victim Glenn Quinn.
The 47-year-old was beaten to death by paramilitaries in Carrickfergus in January 2020.
"This threat appears to have been issued because of my support for the Quinn family a year on from the brutal murder of Glenn Quinn," Mrs Foster said.
"My thoughts and support remains with the Quinn family who have so bravely stood up to continued intimidation.
"This threat is simply reflection of what an innocent family have faced for so long now.
"There must be no place for such behaviour in any free society and we all must stand against those criminal gangs which continue to operate within our community."
DUP MP Gavin Robinson said: "Everyone will stand with the First Minister and particularly with the Quinn family in the face of such threats.
"It is important that we all continue to shine a light on such groups who exist for nothing more than their own criminal purposes."
The threat has been condemned by politicians from across rival parties.
Ulster Unionist leader Steve Aiken called the threat against Mrs Foster "abhorrent".
"Yet again the so-called 'defenders' of Ulster threaten the democratic process," he said.
"The Ulster Unionist Party expresses our support for Arlene Foster in facing down these threats and encourages the community to assist the police so that they have the evidence to end the reign of these thugs, once and for all. We need to see action taken by the PSNI.
"We must all stand together to see that justice is delivered for the Quinn family."
SDLP leader Colum Eastwood also expressed his support.
"The threats against Arlene Foster made by the South East Antrim UDA are reprehensible. No one should have to live under the threat of violence, regardless of who you are," he said.
"The Quinn family have had to endure similar attempts to intimidate them over the course of the past year as they seek justice. Those responsible have no support.
"It doesn't matter what banner they operate under, what their motivation is or who they think they're serving, the faceless thugs who have exerted paramilitary influence in our communities need to go away for good.
"The PSNI needs to disrupt and dismantle these gangs. They have no place in our society and it is far beyond time that they were taken apart."
