The numbers approved for a mortgage in May have gone up, but at a slower pace than the same month last year.
This is due to Central Bank lending restrictions, experts said.
Figures from the banks show 2,461 potential buyers were approved for a mortgage in May.
This was up 20pc on the figure for the same month last year, according to the Irish Banking and Payments Federation.
Experts said this was slower than the rises in the numbers approved for a home loan earlier in the year.
In February the Central Bank introduced limits on lending, in a move it called macro-prudential rules.
Economist with Goodbody Stockbrokers Eamonn Hughes said: "The surge in mortgage approvals ahead of the implementation of the new Central Bank macro-prudential rules was always likely to result in a slowdown once the rules were implemented."
Not all of those approved for a mortgage will end up drawing one down as they may be outbid for a property.
The banks said some €452m in mortgages was approved per month in the three months to May.
Most of this was for home purchases.
The value of mortgage approvals increased by 26.3pc year-on-year and by 2.5pc month-on-month.
The average value of a mortgage approved by the banks in May was €183,665.
Meanwhile, the trend of moderate house price growth, which was evident in the first three months of the year, has continued into the second quarter, according to a house price survey from MyHome.ie
It said asking prices rose by 1.7pc in the second quarter and are now up 6.1pc on the year.
In Dublin the rate of increase was higher, at 2.3pc on the quarter, and 10.4pc on the year, according to MyHome.ie.
According to the survey, the mix adjusted asking price for a house nationally is €202,000, while in Dublin it is €282,000.
Author of the report, Conall Mac Coille, chief economist at Davy Stockbrokers, said the MyHome.ie data points to a modest increase in house prices for the remainder of 2015.
"New instructions give the best lead indicator on house prices and while the outlook remains uncertain, we believe house prices look set to rise by close to 10pc for the calendar year," he said.
Mr Mac Coille said the figures for new instructions indicate that annual price inflation is likely to slow towards 5pc by the end of the year.
"This is not a negative given that wages have not kept pace with house prices, stretching affordability," he added.
He said cash buyers still account for over half of transactions in the housing market.
But it will probably be the second half of the year before the full impact of cash buyers becomes apparent.