Average prices for homes here rose 0.3% between April and June, according to Ireland's largest estate agents.
Sherry FitzGerald said the increase brings overall house price inflation since January to 0.6%.
That represents a slower rate of growth that in the same period last year, where prices increased by 3.2%.
"The latest data on house price performance reveals a continued moderation in price inflation most notably in Dublin," said Marian Finnegan, Chief Economist at Sherry FitzGerald.
"The ongoing impact of a restricted mortgage market, due to the tightening of the lending policy introduced towards the end of 2017 has restricted affordability and subsequently price inflation."
"This is more notable in higher value location such as Dublin, Wicklow and the regional centres. This trend of low price growth is likely to remain a feature of the market."
The capital has recorded very modest house price gains in the year so far, with just a 0.1% increase, compared to 3.3% in the same period a year ago.
Limerick was the regional centre outside Dublin experiencing the most substantial house price inflation, according to Sherry FitzGerald, running at 2.2% since January.
Nationally, excluding Dublin, prices crept 1.3% higher in the year to date, compared to growth of 3.1% recorded in the same period in 2018.
The analysis says modest increases in the volume of new house sales in the opening quarter could be a result of delayed closings due to new building controls and capacity constraints in the industry.
Around 90% of all new properties which sold in the first three months of this year changed hands for less than €500,000 in value.
This points to the success of the 'Help to Buy’ scheme in delivering much needed starter homes into the market, Sherry FitzGerald says.
In total the value of residential property transacted in the opening quarter of 2019 came to €3.2 billion.