Bullets have been sent to news studios in Belfast with the names and details of six people, including Sinn Fein party president Gerry Adams and the party’s senior press officer Richard McAuley.
The threat sent to UTV television claimed to be from the Red Hand Commandos, a cover name normally used by the unionist paramilitary UDA.
Last week, unionist paramilitaries again threatened Sinn Fein members in County Fermanagh as part of an ongoing intimidation campaign in the area.
A brick was thrown through a window of Sinn Fein offices in Lisnaskea on Thursday last week. A note on it threatened to kill three party members, including elected representatives.
The same office was badly damaged in an arson attack earlier this month.
Sinn Fein West Belfast Assembly member Paul Maskey said the recent threats were “a sinister development” and “not in isolation.”
“I urge Unionist politicians to show mature leadership, condemn these threats and use whatever influence they have to stop these actions,” he said.
Fermanagh MP Sinn Fein’s Michelle Gildernew has lodged a complaint with the Dublin government after the PSNI failed to provide information on the death threat against her.
Ms Gildernew said she was unable to take preventative action because the PSNI did not detail the nature of the danger posed by the Red Hand Defenders group.
The Agriculture minister in the Six County Executive is among those identified in death threats by the Red Hand Defenders as being part of a “pan-nationalist front” in the area. The same group claimed the assassination of human rights lawyer Rosemary Nelson in 1999.
“I have spoken with senior members of the PSNI about this,” said Ms Gildernew.
“The PSNI have refused to provide information about the extent and nature of the loyalist death threats against me and other party members in the Fermanagh area.
“This conceivably heightens the risk because I am unable to take preventative measures. This is totally unacceptable.”
Sinn Fein Fermanagh Councillor Thomas O’Reilly urged unionist representatives and clergymen to help stop the threats.
He said: “This is obviously very worrying. Less than two weeks ago the offices in Lisnaskea were badly damaged in a fire and now there is this threat against three named individuals and the wider nationalist republican community in this area.
“There is a clear responsibility on local politicians, community and church leaders to use their influence within the unionist/loyalist community to come out against all sectarian threats or attacks.”
Meanwhile, a petrol bomb attack on the Derry Sinn Fein Constituency Office last week is also being blamed on unionist paramilitaries.
Local Sinn Fein Assembly member Martina Anderson said the attack would not prevent Sinn Fein activists and elected representatives from “delivering a first class constituency service to the community”.