The total number of trips into Ireland between April and June of this year increased by 10.3% to 2,344,900 compared to the same period in 2014.
Trips by residents of Britain rose by 5.8% to 886,200, while visits by residents of other European countries increased by 10.4% to 850,900.
Meanwhile, trips by residents of North America to Ireland increased by 18.3% to 468,100, and trips to Ireland from other areas were up 13.9% to 139,700.
The total number of overseas trips made by Irish residents between April and June increased by 7.6% to 1,927,500.
Overall, the total number of overseas trips to and from Ireland during the second quarter rose by 9.1% to 4,272,500, when compared with the same period 12 months earlier.
Speaking following the release of the figures, Minister for Tourism Paschal Donohoe said: "Today's figures, which are the best on record for this period, are up an encouraging 11.7% compared to the first six months of 2014.
"This is excellent news for everybody involved in Irish tourism and reflects the hard work carried out by Government and all those involved in the tourism industry."
Minister of State for Tourism Michael Ring said that Asia and Australia are being targeted, but that Britain continues to be the best market for tourism.
Speaking on RTÉ's News At One, he said that tourism is playing a role in the economic recovery of the country and that Ireland must stay competitive.
On the proposed increase in the minimum wage, he said he does not believe it will have any effect on businesses in the tourism sector.
Many people in the industry are paying more than the minimum wage, he said.
He said he hopes the lower VAT rate will remain at 9% and that travel tax will stay removed.
Mr Ring also said he would like to introduce a tax-break scheme for seaside towns and is in discussions with Minister for Finance Michael Noonan about that.
