The Revenue Commissioners is investigating 93 cases of suspected non-payment of the domicile levy involving 63 wealthy Irish individuals.
The €200,000 levy was introduced in the 2010 Budget amid concern that high net worth individuals were not paying their fair share of tax.
The levy is charged on an individual with a worldwide income of €1m, whose tax liability is less than €200,000 and whose Irish property is greater in value than €5m.
Records obtained by RTÉ's Morning Ireland under the Freedom of Information Act show that a compliance programme was conducted by Revenue this year relating to individuals potentially liable for the levy in the years 2010, 2011, and 2012.
It identified 256 cases involving individuals potentially liable for the levy, of which 93 are still being pursued.
Revenue said the 93 open cases are subject to ongoing compliance activity.
It also said it has collected €9,828,683 since the levy was introduced in 2010.
The payments were made by 31 individuals, 16 of whom only made payments as a result of compliance activity.
Fianna Fáil leader Micheál Martin said it is "unacceptable" that people had not paid the levy.
Speaking on RTÉ's Morning Ireland, he said: "Revenue has the powers and have the legislative capacity to go after those who are not paying their due tax.
"That is something I welcome and I welcome the fact that Revenue are pursuing this tenaciously and we would support them in every way."
