Almost 5,000 mortgages to the value of over €1.1 billion were approved in May, the latest figures from Banking and Payments Federation Ireland show.
Over 51% of these were for first-time buyers while mover purchasers accounted for 26.3%.
Today's figures show that the volume of approvals rose by almost 20% month-on-month and by 10% year-on-year.
Meanwhile, the value of mortgage approvals rose by 22.1% month-on-month and by 12.1% year-on-year.
The BPFI also said that re-mortgage/switching approvals rose on a year-on-year basis by 7.5% in volume and by 5.1% in value terms.
Felix O'Regan, Director of Public Affairs at the BPFI, said that mortgage approvals in May showed a significant increase in both volume and value compared to the previous month as well as the previous year.
"In line with the broad pattern over recent months this uplift in activity is very evident in the first-time buyer segment of the market, which continues to account for just over half of all mortgage approvals," he said.
"All in all, these approval figures point to a good pipeline of mortgage drawdown activity," he added.
Conall Mac Coille, chief economist with Davy, said the market was bouncing back after some weakness earlier in the year as fears around Brexit put people off going into the housing market.
"We've seen a rebound in residential transactions coming into the summer months. The other issue is that last year we saw a squeeze on people who could get an exemption above 3.5 times income. If we look at first time buyer average approval at the moment, at €238,000 it's up 5% on last year", Mr Mac Coille said.
"It looks like some of that squeeze that we saw in the market last year is going away. The banks don't need to squeeze lending because of the changes in the rules 18 months ago. People are being approved for higher levels of mortgage debt and in time that will breed higher inflation," the economist added.
He said suggestions that uncertainty around the future of the help to buy scheme was contributing to a slowdown in house building had yet to feed through to the figures.
"Completions in the first quarter were up. Commencements are up to about 23,000 in the 12 months to April. We're not seeing any slowdown in the data on home building. We're still at depressed levels and it's picking up."
In terms of the help to buy scheme, Conall Mac Coille said once such programmes are implemented, they're hard to take away without resulting in politically difficult decisions.
"It would cause a bit of disruption and dislocation in the market. If a builder bought land expecting to achieve a particular price for the homes he's going to sell, he would have to cut that back," he stated.