Demand for Irish identity papers hit new heights last year with 733,060 passports issued.
The European Championships in France, more Irish holidaymakers going abroad and high levels of renewals from a historical spike in 2006 also played a part in the record year.
Mr Flanagan said he expects the growth in demand to continue over the coming years.
A breakdown of applications showed 461,911 passports were issued to adults.
Outside of Dublin the biggest demand came at the consulate in New York from where 7,205 passports were issued.
Elsewhere, Canberra was the busiest embassy for ID papers for youngsters with more than 490 applications while there were more than 300 applications for passports for under threes in Abu Dhabi.
Closer to home the Department of Foreign Affairs reported 67,972 applications from people in Northern Ireland and another 64,996 from people with Irish roots in Great Britain for 2016.
Mr Flanagan said: “The department has worked hard in recent years to ensure we provide a modern, secure and quick passport service.
“However, it remains very important that prospective travellers check the validity of their passport before booking a trip overseas and apply for their passport in plenty of time. Delays are often caused by incomplete applications so it’s important to ensure applications are correct and complete before submission.”
The passport office’s figures for 2016 showed that May was the busiest month as close to 100,000 applications came in. There were also surges in August, October and November.
Anyone born on the island of Ireland or whose parents are Irish automatically qualifies for citizenship.
In some cases, those who have an Irish grandparent can also apply - known in some quarters as the Cascarino effect after Jack Charlton’s exploits as manager of the Republic of Ireland football team in the late 1980s and early 1990s.
One in four people in Britain is said to have Irish heritage.
Diplomatic staff in Dublin were forced to issue an appeal for calm in the days following the Brexit vote after post offices ran out of Irish passport application forms because of an initial surge.