The number of properties sitting on the market remains very low
National house prices have increased by more than €2,000 a month in the last year.
The latest House Price Report from Daft.ie shows the 4.3% increase in the second quarter of 2017 matched the increase seen in the first quarter.
The national average list price during the second quarter was €240,000 - 11.7% higher than a year previously and over €75,000 higher than its lowest point.
The annual rate of inflation in Dublin, which was 12.3% in the year to June, is now higher then the rate in the rest of the country (11.3%) for the first time since early 2015.
In Galway, Limerick and Waterford cities, the annual change in prices is even higher and is closer to 15%, while in Cork city, the rate is 9.2%.
Elsewhere, the average rate of inflation was 11.2%, but this varied from 7.8% in Connacht-Ulster to 13.4% in Leinster (outside Dublin).
The number of properties being listed continues to rise.
Over 6,000 properties were listed for sale in May, the highest monthly total since the middle of 2008.
But due to strong demand, the total number sitting on the market remains very low, at just 22,400 on June 1st.
Daft says while this is higher than three months earlier, it is 11% lower than on the same date in 2016 and roughly two-thirds below the 2008 peak.
Commenting on the figures, report author Ronan Lyons said: "After two years where Central Bank rules had capped house price growth in the capital, the relaxation of those rules has helped drive prices further up.
"Whereas non-urban markets had driven house price growth in 2015 and 2016, Dublin again is seeing increases that are above the national average.
"With each passing quarter, the imperative becomes even greater to address the high construction costs that are limiting the ability of supply to meet strong demand."
Average list price and year-on-year change:
Read the report in full here
Homeless charity Focus Ireland has expressed concern over rising rents.
Advocacy manager with the charity, Roughan MacNamara, said: "The findings of the DAFT.ie report clearly show the Rent Pressure Zones are not working.
"Rents nationwide have now reaching an all time record of an average of €1,131 as national rents are now 10% higher than 2008 rents.
"While the Rent Pressure Zones have helped curtail rent increases for some sitting tenants the legislation to control rents between tenancies is still far too easy for landlords to ignore.
The charity says there is no monitoring to check if landlords are abiding by the 4% rent increase cap when one tenant leaves and a new tenant signs a new lease.
"It seems these rules are being widely ignored", Mr MacNamara said.
Focus Ireland has called for effective penalties put in place to punish any landlords caught breaking the rent cap in a rent pressure zone.
"Our frontline staff are still dealing with people who have become homeless from the rental sector as rents have been hiked up and they can't afford them.
"There needs to be a much wider range of Government actions taken to keep protecting tenants and keep them in their homes."