Turkish workers of Gama Construction have accused Minister of State for Overseas Development Conor Lenihan of adding "insult to injury" with his "stick to the kebabs" remark in the Dáil this week.
They claimed Mr Lenihan had likened them to "a piece of meat" when he made the comment to Socialist Party TD Joe Higgins.
One of the workers, Rafet Gokturk, said the remark was "a big insult" and he and his colleagues were "very offended" by it.
Speaking through an interpreter yesterday, Mr Gokturk said the Gama employees were already struggling against injustice in Ireland and were trying to vindicate their rights.
"And while we are in this difficult situation along comes a Minister with responsibility for human rights and aid to foreign countries and makes this kind of remark as if we were just a piece of meat."
The remark had added insult to the injury already suffered by the Gama workers in Ireland.
Mr Gokturk, speaking at a press conference in Dublin called in relation to other Gama issues, said the insult had been delivered to the workers through Mr Lenihan's attack on Mr Higgins. Mr Lenihan should apologise to the workers, he said.
Mr Lenihan apologised in the Dáil after making the remark to Mr Higgins during a debate on Aer Lingus on Wednesday. He said he regretted the comment and apologised sincerely "if any offence was taken from the remarks I made".
Taoiseach Bertie Ahern has said the apology by Mr Lenihan was enough and that the matter was now over.
Minister for Foreign Affairs Dermot Ahern also said he did not think Mr Lenihan needed to re-evaluate his position after the remarks.