Northern Ireland Deputy First Minister Martin McGuinness has rebuked Lord Tebbit for saying he hopes Mr McGuinness is shot in the back for attending a state banquet at the invitation of Queen Elizabeth II.
Mr McGuinness said the reaction of the former Conservative chairman to his historic visit to the queen's official residence and private home at Windsor was "not fitting" for someone who holds high political office.
"Norman Tebbit too and his family have been very badly hurt by the conflict," he said.
"I absolutely understand that. Obviously the sentiments that he has expressed, I think, are not fitting for someone in the elected position he has been in for a very long time."
The British peer was injured along with his wife during the 1984 IRA bombing of the Grand Hotel in Brighton, which targeted the Conservative Party conference.
His latest remarks have been described by a senior Sinn Féin official Danny Morrison as advocating the assassination of Northern Ireland's Deputy First Minister.
However, Mr McGuinness told RTÉ's Today with Sean O'Rourke he would not be drawn into a row over the comments.
"I'm not going to make an issue of it," he said.
"Other people have certainly raised it with me, and some people have advocated that I should make an issue of it - I don't intend to do so."
Mr Tebbit said the queen had no choice about Mr McGuinness attending the state banquet at Windsor Castle last night in honour of the visit of President Michael D Higgins.
He said: "There's always the possibility that a member of the Real IRA will be so outraged by Mr McGuinness bowing to the Queen that they might shoot him in the back for it.
"We can but hope."
Mr McGuinness said he had no qualms about standing and joining in a toast to the queen, the Duke of Edinburgh and the people of the UK as an orchestra played God Save the Queen during the dinner.
"I went to Windsor Castle last night as an unapologetic Irish republican, and I'm still an unapologetic Irish republican this morning," he said.
"So I think it is possible to do these things, particularly in the context of a very clear indicator that others - such as Queen Elizabeth in her visit to our country, both to Belfast and to the south - were prepared to show impressive leadership in the context of conflict resolution and acts of reconciliation."
He added: "I believe I have the overwhelming support of the people of Ireland for what I did last night."
Mr McGuinness said he understood the pain of people affected by the Troubles and defended their right to protest at his attendance.
"I understand that people are hurting as a result of the fall-out from the conflict and many in my community - in the republican, nationalist community - are also hurting as a result of the conflict," he said.
"Different sections of that community come to this at different speeds."