Sinn Féin's Michelle O'Neill says police have informed her that dissident republicans are planning an attack against her and Gerry Kelly.
Ms O'Neil said the threat had been issued after they attended a PSNI recruitment event last week.
"I have been told by the PSNI that they have intelligence that dissident republicans are planning an attack against myself and Gerry Kelly," Ms O'Neill said.
"These people have nothing to offer society. These people have clearly intent to attack myself and Gerry, our families. We are also aware this comes on the back of both myself and Gerry attending the PSNI recruitment fair last week.
"So let me be very clear, dissident republicans have no strategy, they have no plan, they have no progress towards Irish unity and I think this intelligence comes at a time when we have never been closer to Irish unity.
"I will not be deterred. Gerry Kelly will not be deterred. Sinn Féin will not be deterred from trying to build a better society," the deputy first minister added.
First Minister Arlene Foster condemned those behind death threats.
"We live in a democracy. The ballot box is how we effect change, not through the bomb or bullet," she said.
"Whether in 1970, 1980, 1990 or 2020, violence from every hue must be condemned. There is no place for threats or violence."
SDLP leader Colum Eastwood condemned the threats against Ms O'Neill and Mr Kelly as an "attack not just on one party but on the peace we've all fought for".
"Those behind it are setting themselves against the Irish people and they will never win.
"My thoughts are with Michelle, Gerry and their families today."
