The Department of Foreign Affairs has said that due to an increase in Irish passport applications, the Passport Office is recruiting extra staff.
In a statement to RTÉ's Morning Ireland, the department said Brexit has resulted in a rise in submissions from Northern Ireland and Britain.
Anyone who has a parent or grandparent born in Ireland is entitled to an Irish passport.
Latest figures from the Department of Foreign Affairs show that applications from the UK were up 74% in January compared to the same time last year.
In January this year, over 7,000 people from Northern Ireland applied for an Irish passport, up from 3,973 in the same month last year.
In Britain there was a jump of 71%, with 6,000 applying this January.
Last year passport applications from Northern Ireland saw an increase of 26.5% over 2015 to 67,972, while application levels from Britain increased by 40.6% to 64,996.
Opportunities as an EU citizen include living and working anywhere within the union, a student exchange programme, and having access to healthcare when travelling.
However, there is now a chance those perks will disappear for British citizens following Brexit.
Minister for Foreign Affairs Charlie Flanagan said that to alleviate pressure on the passport service, the department is recruiting over 230 temporary staff, over half of whom are already in place.
He also added that an online adult passport renewal system will be rolled out before the end of March to ease demands.
Mr Flanagan said: "Early indicators in 2017 are showing that increased demand for passports is likely to be sustained, certainly in the immediate future. I am carefully monitoring passport services."
He continued: "It is vital that applicants check the validity of their passports before booking travel, apply in good time, ensure forms are correctly completed, and consult the different turnaround times for different categories of passport."
Mr Flanagan was responding to comments by Labour MP Gisela Stuart, who co-chaired the Vote Leave campaign in the UK, that the high number of Britons applying for Irish passports will be a "challenge" for both the UK and Ireland.
Ms Stuart said that it is an issue politicians have to respond to.
The German-born Member of Parliament, who had to give up her German citizenship on election to the House of Commons in the 1990s as it was not permitted for members to retain two nationalities, said there are "more people living on mainland United Kingdom who have the right to Irish citizenship than there are actually currently Irish citizens in Ireland".
She said the rise in the number of Britons applying for Irish passports is an "understandable reaction" due to a period of uncertainly but "that doesn't have to be".
Just under 65,000 people applied for an Irish passport in 2016.