Fianna Fáil's justice spokesperson has branded comments on Twitter by his party colleague Lorraine Clifford-Lee as "offensive, silly and inappropriate".
Jim O'Callaghan said the Senator's tweets, which have been deleted from her Twitter account, displayed prejudice towards Travellers and she has bridges to build.
However, Mr O'Callaghan said that Senator Clifford-Lee has apologised and he believes in redemption.
Fine Gael has again called on the Senator to answer questions about the tweets.
Fine Gael Senator Gabrielle McFadden said Ms Clifford-Lee must answer if she accepts that some of her tweets were targeting "members of minority communities and are therefore racist?"
"The excuse that she was not a public representative when she wrote these tweets is no defence. She was a grown woman and a fully qualified solicitor when she wrote these slurs," Ms McFadden said.
Jim O'Callaghan says Lorraine Clifford Lee’s tweets were: inappropriate, silly, offensive and displayed prejudice towards travellers, but he believes in redemption and says she has apologised. @rtenews pic.twitter.com/lqg1GAcXZR— Mícheál Lehane (@MichealLehane) November 12, 2019
The tweets include one in July 2011 in which Ms Clifford-Lee said: "Just doing up inventory of items in my car when it was stolen by some knacker. I think I am going to cry."
In another, dated June 2011, she described some clothes as being "like something from a traveller wedding".
Yesterday, Fianna Fáil said that it did not have any plans to discipline Ms Clifford-Lee over the tweets.
A spokesperson said that the party does not condone the tweets and believe they were inappropriate.
"However Senator Clifford-Lee has acknowledged her mistakes, has apologised and deeply regrets them," the party added.
Minister for Employment Affairs and Social Protection Regina Doherty said Ms Clifford-Lee is "in a bit of a pickle. None of us are perfect".
She said Ms Clifford-Lee needs to come out and apologise and have a conversation with Pavee Point.
She said ignoring it will not make it go away.
Fine Gael TD Joe McHugh said there is a wide debate going on about how social media is handled and it can be used as a weapon.
He said, "in this instance it was used as a weapon and it's totally inappropriate".
Ms Clifford-Lee, who has been a Senator since 2016, is running in the by-election for the Dublin Fingal constituency.
Other declared candidates include Dr James Reilly, who is running for Fine Gael, Ann Graves for Sinn Féin, Duncan Smith for Labour, Joe O'Brien for the Green Party and Independent Gemma O'Doherty.
Fianna Fáil said that it will continue to support Ms Clifford-Lee as she competes for a seat in the Dáil.
Additional reporting Mary Regan