More than 2.26 million people travelled to Ireland in the three months to the end of August, according to the Central Statistics Office, a 6.7% increase on the same period of 2012.
Trips from residents of North America saw the most significant increase during that time, rising 19.9% to 437,900.
The CSO figures show a 4.7% rise in British residents travelling to Ireland during the three months, while the number of trips from residents of other European countries rose by 0.9%.
Overall, European residents accounted for 1.67 million trips to Ireland between June and August 2013 – almost two thirds of all trips made.
Meanwhile, there was a 17.6% increase in the number of trips being made by residents outside of Europe and North America.
In the year so far there has been a 6.5% increase in the number of trips to Ireland, with 4.75 million people coming to the country in the first nine months.
Nearly two million of those have come from Britain, 1.7 million from the rest of Europe and over 800,000 from North America.
Separately, the number of overseas trips being made by Irish residents also increased between June and August.
Almost 2.14 million Irish residents travelled abroad during those three months, compared to 2.07 million in the same period of 2012.
More than 4.4 million overseas trips have been made by Irish residents in the year so far – an increase of 30,000 on the first nine months of last year.