More than 2.38 million people travelled to Ireland between March and May, according to the Central Statistics Office, an increase of 10.3% on the same period of 2015.
British visitors made up the single biggest proportion of trips at 990,400 – which was up 9.3% year-on-year.
Meanwhile there were 861,600 visitors from other European countries – up 9.2%.
North American visitors accounted for 414,200 trips in the three month period – up 19.3% - however trips from other areas of the world fell by 0.3% to 116,600.
The figures bring to 3.46 million the number of visits made to Ireland in the first five months of the year – a rise of more than 13.7% year-on-year.
There was also an increase in the number of Irish residents making overseas trips, with 1.76 million travelling abroad between March and May. That is an increase of 8.4% on last year.
In the first five months of the year Irish residents made 2.67 million overseas trips – up 7.8% year-on-year.
Minister for Transport, Tourism & Sport Shane Ross said: "Today's figures reflect an excellent performance for overseas visit numbers with an increase of 13.7% in the first five months of 2016, compared to the same period in 2015.
"These figures once again confirm that our tourism sector is continuing to perform well and we are on track for another excellent year.
"Of course the result of the referendum in the United Kingdom shows how events outside our control can potentially impact on our strong performance.
"Nevertheless, the Great Britain market will remain of significant importance to Irish tourism in the short, medium and long term," the minister added.
