Leo Varadkar says the Government wants "all eligible parents to apply for this new benefit"
More than 3,500 fathers have been approved for the new entitlement of paternity benefit.
The scheme was launched on September 1st, offering new dads €230 per week for a fortnight.
The Department of Social Protection also says the number of applications almost doubled between September and October as awareness of the entitlement grew.
Of the 3,575 claims, most were from employees, with 267 from the self-employed.
Minister Leo Varadkar said: "We want all eligible parents to apply for this new benefit as we believe it’s important that new dads get to spend more time with their children.
“I’d like to remind any new dads who haven’t applied yet that they might still be eligible, as it’s available for up to 26 weeks following the birth of a child born any time after September 1st [...] Remember also that Paternity Benefit is available to parents adopting a child, and to same-sex couples," he added.
To qualify for the payment, applicants must satisfy social insurance contribution conditions, while employees are required to give four weeks’ notice to their employer.