Peter Casey has accused the Taoiseach of going against the spirit of the constitution.
Leo Varadkar was among those who condemned the businessman's comments about Travellers.
And he called on people to send a clear message in Friday's election about anti-Traveller views.
Peter Casey was considering his position in the race over the weekend but has decided not to pull out.
He also does not believe there is anything offensive in what he said.
"There is absolutely nothing offensive about anything I've said, I simply pointed out that we need to treat everyone equally," said Mr Casey.
"How anyone could find that racist is just beyond me.
"For the Taoiseach and the Tánaiste to come out, I find that deeply offensive and hurtful."
He went on to say that Taoiseach Leo Varadkar knows that he is not a racist "yet he came out and said, he interfered in the presidential process.
"He is fully entitled to endorse a party like he has done and that is absolutely his prerogative.
"It is not his prerogative to get involved in the process of the presidency."