Only half as many mortgages were approved last month as during June 2019.
There was a 20% increase on the previous month's figures, according to the Banking and Payments Federation Ireland (BPFI).
During the second quarter of the year, the value of mortgages drawn down was a third less than the same period last year.
The BPFI said the future is difficult to predict as Covid-19 continues to impact on the market.
However, the head of the BPFI has said he is "relatively optimistic" that the Irish mortgage market will recover this year.
"I think it's a consequence of the dysfunctional nature of the housing market right now, given what we've gone through in the last two quarters or so - the last four or five months.
"It's not unusual that there would be this kind of volatility in the figures."
"There's good news and bad news: the bad news is obviously for quarter two of this year, mortgage drawdowns are down about 35% when you compare the figure with quarter two of last year.
"And they're down significantly on quarter two, you could argue that quarter two is probably the worst quarter of the year, given what's happened".
Asked about a hangover into later this year and 2021, Mr Hayes said: "I'd be relatively optimistic at this stage, given that the economy's come out of lockdown.
"People are going back to work, people are now buying and selling houses again, there's more houses coming back on the market.
"There's been a brief reluctance for sellers to put their houses on the market, given the uncertainty that's been there.
"Given that kind of construction backdrop where for three, five months or so we didn't have builders out there - now we have.
"So I think as we get through this year, as those quarters continue, you're likely to see better numbers."
"I hear the comment made by people 'lenders aren't lending' and all the rest of it: quarter two shows that 6,500 mortgages were drawn down by the banks of this country."
Overall, 6,622 new mortgages worth €1,462m were drawn down by borrowers during the second quarter of 2020.
This represents a fall of 34.8% in volume and 35% in value on the corresponding quarter of last year.
First-time buyers (FTBs) remained the single largest segment by volume (49.6%) and by value (50.3%).
A total of 2,263 mortgages were approved in June - 1,059 were for FTBs, while mover purchasers accounted for 557.