Residential property prices have increased in May by 0.5% in the month, and 13.8% in the year.
In Dublin, residential property prices fell by 0.1% last month - but these prices were still 15.2% higher than in May 2014.
Dr John McCartney, director of research at property consultants Savills, says the rate of growth is now slowing in Dublin.
"We may see a further cooling off in price growth from September when all the house hunters with legacy loan approvals have done their deals," he said.
"In the longer term, there could be an offsetting pick-up in investor activity as rising rents are making buy-to-let returns look increasingly more attractive than bank deposits."
Outside of Dublin, residential prices rose by 1.1% in May. At a national level, prices were 37.5% lower than their peak level in 2007.
Dublin house prices were 36.4% lower than their peak, Dublin apartment prices were 41.9% lower - and overall prices in the capital were 38.1% lower than their highest level.
Outside the capital, residential property prices were 40.8% lower than their highest level.
More tourists coming to Irish shores
Other figures released by the Central Statistics Office (CSO) today show trips to Ireland grew by 13.4% for the period of March to May.
The total number of trips to Ireland increased to 2,159,800 - an overall increase of 255,500, compared to the same period 12 months earlier.
Trips by residents of the UK increased by 11.5% to 906,500, while trips by residents of European countries increased by 12.9% to 789,300.
Trips from North America here grew by 17.1%, to 347,100 - while trips to Ireland from other areas increased by 21.5% to 116,900.
And more Irish people are also going abroad - with the total number of overseas trips made during the same period up by 6.5%.