Ulster Unionist members of Fermanagh and Omagh District Council are calling on Taoiseach Micheal Martin to speed up the extradition of Liam Campbell to face weapons smuggling charges.
t a meeting of the council's policy and resources committee earlier this month, Independent councillor Bernice Swift sought support in opposing Campbell's extradition to Lithuania, citing human rights concerns.
During the meeting the chairman, Sinn Fein councillor Stephen McCann, permitted the last-minute notice of the proposal and open debate was not held, with councillors moving quickly into confidential business.
Campbell was found liable in a civil court for the Omagh bomb in August 1998, which claimed the lives of 29 people, including a woman pregnant with twins, and injured 220 others.
The move has left victims of the atrocity "appalled and retraumatised".
The UUP motion to write to Mr Martin urging him to "speedily resolve" Campbell's extradition process is due to be debated by councillors on Thursday night.
Speaking ahead of the meeting, UUP councillor Victor Warrington told the Belfast Telegraph: "The recent proposal by councillor Swift was both insensitive and heartless.
"Let's be honest, this was done under the guise of human rights but in reality it was nothing other than a political stunt.
"If councillor Swift is so worried about individuals' human rights maybe she should look at the families and friends of all those who lost their lives, sustained life-changing injuries and the mental health trauma that has followed the Omagh bomb.
"As a council we should not be getting involved in another country's legal system. We are proposing that the council writes to the offices of An Taoiseach to speedily resolve this process owing to the effect that this in having on the people directly impacted locally.
"It has caused further pain and anguish amongst the relatives of the victims."
Last week DUP members of the council lodged a complaint to the Local Government Commissioner for Standards against councillors Swift and McCann.
They argued that the proposal raised by Ms Swift was not within the council's remit and should not have been accepted by Mr McCann as reasonable business for the council to conduct.
The DUP complaint comes after republican councillor Gary Donnelly indicated he will bring forward the same motion at a meeting of Derry City and Strabane District Council on Thursday.