The Fine Gael leader has said he accepts an apology from a Sinn Féin councillor who said a family man should be running the country and that Leo Varadkar's Indian heritage meant he is separated from the history of Ireland.
Mr Varadkar was questioned about the remarks made by Paddy Holohan during a visit to Co Longford this evening.
"I understand that he has apologised in the fast few hours and that's good enough for me," Mr Varadkar said.
Mr Holohan, a councillor from West Dublin and former MMA fighter, made the comments during two separate episodes of his podcast series entitled "No Shame".
In a Twitter post, Paddy Holohan later said his remarks had been misinterpreted and apologised.
He said they were "not in any way meant the way they have been portrayed".
Mr Varadkar said: "In terms of the wider issue I think anyone in Ireland who's from a minority background, whether mixed race or gay or lesbian, has experienced some form or racism or homophobia in their lives.
"I'm fortunate in that I haven't received too much of that, I know it's been a lot worse for a lot many other people.
"But I think as a wider issue, one of the things I would like to do if I'm re-elected as taoiseach is to run another cross-government campaign against racism.
"We did that before and I think you can never do enough. We just need to raise awareness of the issue and make sure that we have a properly united country, no matter whether you're a man or a woman, no matter what background you come from, whether you're a member of the the travelling community or not, or who you love. None of those things should matter in the kind of society that I believe in."
Sinn Féin President Mary Lou Donald has said she is satisfied that Cllr Holohan has apologised.
She said the party had insisted he apologised for the comments, he had done that, and the apology was the right thing to do.
Ms McDonald said she believed Mr Holohan said he was misinterpreted because he was probably frustrated that the remarks gave the impression he held views different to the ones he is associated with.
"I think Paddy is probably frustrated at the fact that's he known for being very approachable, a very open minded and a very kind person.
"Unfortunately the remarks that he has made have given the impression that he holds other views and I imagine that what he meant, although I can't speak for him, what he means in terms of interpretation."
She said the best of people can make a mistake and speak out of turn but the gracious thing to do and the thing of integrity is to apologise and he had done that.
Earlier, Sinn Féin said the comments were not the views of the party.
The Sinn Fein President Mary Lou Donald has said shes satisfied that Councillor Paddy Holohan has apologized for the comments he made about the Taoiseach. She said the party had insisted he apologized, that he had done that and that it was the right thing to do @rtenews pic.twitter.com/HOqS8BLbxp— Samantha Libreri (@SamanthaLibreri) January 16, 2020
Mr Holohan said while he did not have anything against Mr Varadkar, he believed a family man with children would be best equipped to run the country because it would give them a better understanding of the policies they are implementing.
Speaking during two separate episodes of his podcast series entitled 'No Shame', the 31-year-old councillor for Tallaght South also said that Mr Varadkar was "separated" from the history of Ireland because his grandfather was Indian.
In one episode of the podcast published earlier this month, Mr Holohan said: "We need people running the country, and not against Leo or anything like that but to me I want a family man running the country, I want somebody that knows what it’s like to have kids, maybe hopefully boys and girls so when you’re creating the policies and all of the stuff that goes on that you’re like, right it makes sense."
He continued: "The man that is a family man, goes to work, looks after his kids, has came up through the system, has experience ... someone who knows what the masses or people are going through."
In another recent episode, he said: "It bugs me to death to understand that he [Leo Varadkar] leads this country and that he's so separated not even from society now but he's so separated from the history of this country."
He added: "Leo Varadkar’s blood obviously runs to India so his great grandfather is not part of the history of this country ... now Leo obviously he’s an Irish citizen, but his passion doesn’t go back to the times when our passion goes back to.
"So we’re in a situation where we have a leader that’s not only separated from the history of the country but separated from the classes in the country now."
Additional reporting Samantha Libreri