Justice Minister Charlie Flanagan has moved to distance himself from Fine Gaeler Verona Murphy.
Mr Flanagan said he wants to “disassociate completely” from her controversial remarks.
There was a public outcry this week after it emerged that the Wexford by-election candidate had made a series of statements on the campaign trail which were later branded racist in the Dail.
They included claims that four-year-old asylum seekers coming here could be influenced by ISIS and need to be "deprogrammed."
There has been turmoil in Fine Gael over what to do about the controversy, with many privately calling for her to be removed from the party ticket.
But the party top brass, including Taoiseach Leo Varadkar, had backed her, up until now.
Mr Flanagan has told the Dáil on Wednesday morning that he can’t stand by her remarks.
“On the Deputy's remark regarding unacceptable commentary in the course of the by-elections which are under way, I wish to categorically dissociate myself from comments made by Ms Verona Murphy, a Fine Gael candidate in Wexford", he said.
“I am sure Deputy O'Callaghan will do likewise in respect of the remarks of a candidate standing for Fianna Fáíl in another part of the country.
“It is incumbent on all Members to ensure that unacceptable commentary is treated as such.
“In that regard, I note certain apologies given by the candidates involved.”
Mr Flanagan was responding to Fianna Fáil justice spokesman, Jim O’Callaghan, who raised the issue during Questions to the Minister.
He said: “We need to remind all people, particularly those in the political domain, that it is a criminal offence to publish written material that is threatening, abusive or insulting and is intended or likely to stir up hatred against groups because of their race, colour, religion or national origin.
“That should be brought to the attention of certain figures in the Minister's party, given their recent utterances.”
