Peter Casey has said he received “thousands” of messages asking him not to pull out of the presidential race.
The Derry-born businessman commands around 2% of the vote and is trailing the other five candidates, polling has shown.
He was criticised after saying Travellers should not be treated as members of an ethnic minority.
On Sunday he added: “I respect the Travellers’ culture and traditions, but I will always think them first and foremost as Irish too.
“If that is wrong, I am not apologising.”
He also touched on issues like homelessness and rural broadband during a lengthy message posted on Twitter.
Mr Casey said hard working taxpayers should be acknowledged and rewarded.
He said, if elected, he could “influence” the Government.
He alleged: “Ireland is slowly becoming a welfare-dependant state, with a sense of entitlement.
“Politicians are focusing all their interests on welfare and social housing but have forgotten about the bill payers.”
The number of long-term unemployed on the Live Register at the end of September was 86,406, which equated to an annual decrease of nearly 18%.
Mr Casey asked: “Where is the incentive to work in this country?
“We have become a nation of people who expect, no demand that the (state) provide them with homes, provide all sorts of social benefits.
“As proud Irish people, we are better than that.”
- Press Association