The Justice Minister and the Garda Commissioner are being urged to flood the Cavan-Fermanagh border with resources to end the intimidation against Quinn Industrial Holdings (QIH).
The directors of the company say they are not surprised to receive yet another death threat, which follows the vicious attack and torturing of their colleague Kevin Lunney last month.
A letter states this is their "last warning" to quit or else they face a "permanent solution."
It also threatens to target Cavan County Council staff who remove posters in the area aimed at the company's directors.
Local Fianna Fáil TD Brendan Smith has said full cross-border resources are vital.
Mr Smith said: "Every possible resource must be put into these investigations to ensure that the people responsible for this deplorable and reprehensible behaviour are brought to justice"
He added that the directors and staff at QIH should be let "go about their business."
Earlier: Quinn directors heartened by support as news of fresh death threats emerge
The chief executive at Quinn Industrial Holdings (QIH), Liam McCaffrey, has said he and his fellow directors have been heartened by the support of customers, staff and the community
The directors received a second death threat on Monday, warning them that they “haven’t learned your lesson” from last month’s abduction and torture of one of its executives
The threat came in the form of a letter, sent to The Irish News and shared with directors of QIH late on Monday. It claims to be the “last warning” to the five local managers of the company to resign or face a “permanent solution”.
Referring to the kidnapping and violent attack on Mr Lunney on September 17, the letter warns that the perpetrators “could have killed him very easily” if they had wanted to.
Mr McCaffrey told RTÉ radio’s Morning Ireland that he was informed of the threat by a PSNI sergeant at his home on Monday evening and since then “there has been a lot of Garda Síochana and PSNI activity monitoring our homes and workplace.”
It was difficult to deal with a small group of criminals led by a task master, he said.
We just have to trust in the Garda Síochana and PSNI investigations.
It was horrendous for any civilised society to have to operate with such sinister threats, he added.
Earlier on Morning Ireland, Assistant Garda Commission John O’Driscoll said that the Garda Síochana and PSNI were determined to pursue the arrest and prosecution of those responsible.
Mr McCaffrey said that Kevin Lunney was recovering well, and while still in pain, was comforted that staff, management and the community wanted to see back at work.
“There is huge support for him in the community.”