The Fine Gael leader, Mr John Bruton, has had discussions with representatives of the travelling community following controversial remarks by one of the party's councillors, Mr John Flannery, of Mayo.
A spokeswoman for Fine Gael last night confirmed that Mr Bruton had told the travellers' representatives that "swift action" was being taken against the councillor.
"He personally conveyed the earlier decision of the Fine Gael parliamentary party condemning the comments," she added.
The party has initiated disciplinary proceedings against the councillor. A Fine Gael spokesman yesterday said that Mr Flannery was "liable to all sanctions available, including expulsion". However, the spokesman stressed that the party is "obliged, under the rules of natural justice, to go through due process".
In the interim, yesterday's meeting of the Fine Gael parliamentary party agreed, on a motion proposed by Mr Bruton, to unanimously condemn the reported remarks of Mr Flannery. The motion also called on him to withdraw his comments and apologise immediately for the offence caused.
Yesterday Mr Flannery said he would not be "gagged" by his party, but he apologised if his remarks had been taken as racist. This was something he had not intended.
"I reject any suggestion that I am a racist. I am not a racist. Nor did I intend my comments to be taken in that way," he said.
The comments, at a meeting of the Western Health Board on Tuesday, led to a storm of criticism from travellers' groups, politicians and trade unionists.
Mr Flannery said travellers should be tagged with microchips in order to monitor their movements. He claimed they expected everything to be done for them while giving little in return.
He also suggested that travellers lay out sunning themselves like pedigree dogs and should be made to work.
Fine Gael's spokesman on social affairs, Mr Jim O'Keeffe, immediately declared his disgust, saying he was "astounded and appalled " at the reported remarks. On behalf of his party, he said, he repudiated the "racist and inflammatory" remarks.
"The notion of second-class citizenship for any individual or community within Irish society has no place in Fine Gael. Disciplinary proceedings about this matter have been initiated and, following due process, will be dealt with by the executive council of the party," Mr O'Keeffe said.
The travellers' organisation, Pavee Point, said the "inflammatory" remarks attributed to the councillor highlighted the urgent need for protective legislation in Ireland. It demonstrated why travellers and their organisation were "crying out" for the long-awaited Equal Status Bill.
Mr Michael Collins, a spokesman for Pavee Point, demanded Mr Flannery's resignation, adding that this kind of statement was an incitement to hatred and an expression of racism towards travellers.
Yesterday the President, Mrs McAleese, told an audience in the Pavee Point centre in Dublin that the ultimate goal of the traveller community was its inclusion in Irish society as a whole.
"You know yourselves how much work is involved in that process, and how at times it can appear that you are going backwards rather than making progress.
"Unfortunately, many people see the `solution' to the treatment of the travelling community in the assimilation of travellers into their concept of society, while some prefer to opt for the domination method of exclusion, assigning them the status of inferior beings," Mrs McAleese said.
Last night a spokeswoman said the President's visit to Pavee Point, and her scripted address, had been prepared in advance of the councillor's remarks. Mrs McAleese did not refer directly to the controversy, the spokeswoman added.