Government Chief Whip and the Minister of State for the Irish Language Seán Kyne has told RTÉ's The Week in Politics that Verona Murphy's campaign will be reviewed following the by-election in Wexford.
Mr Kyne said a video made by Ms Murphy and shared on her Facebook page was not an official party video and that Fine Gael does not stand by the comments made.
He said the party's national executive review all general election tickets from time to time and "I'm sure following these by-elections it will be no different in Wexford".
Fianna Fáil Deputy Leader Dara Calleary called the video an attack on the media, adding that somebody in Fine Gael had to know the video was being released because she was a party candidate and someone must have been monitoring her Facebook page.
Speaking on the same programme, Sinn Féin's Eoin Ó Broin wanted to know if Fine Gael's central Director of Elections contacted Mr Murphy immediately to get the video removed.
He said that if they failed to get it removed, then that was "tacit consent".
Asked if Verona Murphy's campaign was a problem for the Fine Gael brand, Mr Kyne said candidates can always be removed and that her comments during the campaign will be part of a review following the by-election.
In regard to a Social Democrats motion of no confidence in Minister for Housing Eoghan Murphy next Tuesday, Minister Kyne said they want to make sure the Government survives and the people of Ireland are not facing a Christmas election.
He said the motion was "opportunistic" from the Social Democrats ahead of the by-elections.
Asked whether Fine Gael will be speaking to Independent TD Noel Grealish about the motion, he said the Government would want the support of people, Independents included, and that the idea of a Christmas election would "concentrate minds".
Referring to the same issue, Fianna Fáil's Dara Calleary said his party will abstain on the vote and that they have been very clear that Brexit is the big challenge facing the island and if that goes wrong, it will affect everything: budgets for housing and opportunities for housing and health.
Mr Calleary added this motion is opportunistic with by-elections in mind and that the voters did not respond to that.
Eoin O'Broin, who serves as Sinn Féin's Housing Spokesperson, said it was disingenuous to suggest a vote of no confidence in Housing Minister Eoghan Murphy would precipitate a general election.
He said the motion was about getting a change in housing policy and that Fianna Fáil should "put their money where their mouth is", accusing the party of being opportunistic.
He added that children will continue to be homeless by Fianna Fáil facilitating the Government's budgets.
On the subject of general elections, Minister Kyne said the Taoiseach's preference is in May, but the opposition can also call the general election.
Mr Calleary of Fianna Fáil said his party leaders have signalled the Easter recess would be appropriate, when Brexit is in some sort of shape and St Patrick’s Day is over.
