Almost 5,000 mortgages valued at more than €1.1bn were approved in May.
The latest figures from the Banking and Payments Federation of Ireland show that is up 20% on the previous month, and 10% year-on-year.
First-time buyers accounted for half of all approvals, while mover-purchasers accounted for just over a quarter.
The value of mortgage approvals is also up 22% on the previous month, and 12% over the past 12 months.
Director of public affairs at the BPFI Felix O'Regan said the majority of approvals will likely turn into drawdowns in the near future.
Mr O'Regan said: "Obviously it remains for people, borrowers, having got that approval to draw down that mortgage, but certainly as far as approvals are concerned these are strong numbers.
"And the indications are, given previous trends, that most of those approvals will translate into drawdowns in the weeks and months ahead.