Founder of the Quinn Group, Sean Quinn, has called on those who have threatened the directors of Quinn Industrial Holdings (QIH) to withdraw them.
He also stated that they are not acting in his or his family's name.
Mr Quinn issued his latest condemnation of the campaign against the QIH Directors in response to the latest threat made against them.
Speaking to RTÉ's Prime Time, Sean Quinn said: "I have already unreservedly condemned the acts of violence against Kevin Lunney, which I have previously described as barbaric.
"These further threats directed at members of QIHL are beyond comprehension and I implore that whomever is carrying out these heinous acts to cease immediately".
He said that "the ongoing criminal activity is not serving any purpose for me, for my family, for our community nor for the companies themselves, and is in fact terribly damaging to all involved".
"I call on those who have advanced threats to withdraw them immediately. If they feel that they are doing it in mine or my families name, then they are badly mistaken", Mr Quinn added.
Reacting to the statement, QIH Chief Executive, Liam McCaffrey said that he could only welcome it.
"It's clear and concise and it's not ambiguous," he said.
In his previous condemnations, McCaffrey said Mr Quinn had also seen fit to berate the executives of the group, which he thought was wrong.
"But on this occasion he hasn't, so this statement is to be welcomed", Mr McCaffrey said.
Meanwhile, Minister for Justice Charlie Flanagan has said that the Government is doing everything it can to ease tensions in border areas following the recent attacks and threats in the region.
