Applications for Irish passports from Northern Ireland and Britain have risen by 68% in the first quarter of 2017 compared to the same period last year.
Figures from the Republic's Department of Foreign Affairs showed that applications had risen by 26% overall.
The department had received a record number of overall applications in 2016.
There has been an increase in applications from Britain and Northern Ireland since the UK voted to leave the EU.
An Irish passport would allow its holder to continue to move and work freely within other EU member states once the UK withdraws.
Surge in demand
In 2016, applications from Northern Ireland increased by 27% from the previous year while applications from Britain went up by 42%.
The latest figures show that this trend has continued in the opening months of 2017.
Between January and March this year, 27,898 applications were received from Northern Ireland and 23,181 were received from Britain.
In the corresponding period of 2016, 16,581 applications were received from Northern Ireland and there were 13,722 from Britain.
The Department of Foreign Affairs said the the overall increase in applications was "attributable to a variety of causes including an expanding population and a significant increase in outbound travel in recent years".
"The decision by the UK to leave the EU may also have had some impact, although the department does not ask people why they are applying for a passport, only whether they are eligible."
The Republic's Passport Service had already seen a surge in demand prior to Brexit, due to an increase in outbound travel, the Euro 2016 football championships and new US travel requirements for biometric passports.
People with a parent or grandparent born in Ireland are among those who can apply for an Irish passport.