Traveller rights group Pavee Point says its accepted an apology from Fianna Fáil Senator Lorraine Clifford Lee.
Comments the Fingal by-election candidate made on Twitter a number of years ago have been described as racist, misogynistic and classist.
Speaking after meeting with Pavee Point on Friday morning, Senator Clifford Lee said: "I've said I'm sorry for the offence that it caused - and it clearly did cause offence - and I'll continue to say I'm sorry forever more in relation to that because I am sorry from the bottom of my heart".
She came under fire after a series of tweets she posted in 2011 resurfaced.
In them she made derogatory comments about travellers using words like 'pikey' and 'knacker'.
In another post she described sitting on a bus beside a 'black brazillian dwarf with ginger hair'.
Martin Collins from Pavee Point has accepted her apology - but said issues remain that are a matter for the Fianna Fáil party.
"I think she was extremely remorseful, and she has acknowledged unequivocally the hurt, the offence which has been caused to my community".
"The ultimate arbitrators on this will be the people in Dublin-Fingal on polling day"
Meanwhile, Mr Collins said he is concerned the next Irish general election will be the most toxic and racist yet.
Reporting by Emma Tyrrell
