New figures show that nationally rents in the last three months of last year were almost 7% higher than during the same period of 2017.
But the data from the Residential Tenancies Board (RTB) also shows that rents fell slightly between the end of September and the end of December.
As a result of ongoing increases in the cost of renting in the areas of Navan and Limerick City East, both will be designated Rent Pressure Zones (RPZ).
This is the first time two new areas have been designated RPZs, which limits maximum rent increases there to 4% each year.
"This should help moderate rents in these areas," said Rosalind Carroll, Director of the RTB.
"We would encourage both landlords and tenants to contact us for more information on their rights and obligations and we will be rolling out a targeted information campaign in these areas over the coming weeks."
The Rent Index, compiled by the RTB in conjunction with the Economic and Social Research Institute (ESRI), is based on actual rents paid on nearly 18,000 tenancies that were registered with the RTB.
During the final quarter of last year, average rent nationally was €1,134, up €73 on the same period a year earlier.
However, in a further sign of moderation creeping into the market, rent inflation at the end of the three months to the end of December was -0.3%, compared to 2.3% for the quarter to the end of September.
According to the RTB, this is the first quarter on quarter drop since the first three months of 2017.
"We have seen some moderation in the market in the last two quarters, we would hope with more supply coming on stream and the RTB getting more regulatory powers that we will see further easing of rent inflation in 2019," said Ms Carroll.
Nonetheless, average national rents at the end of 2018 are now 15% higher than at the peak in 2007, and 25% higher in Dublin.
In the capital average rent in the final quarter of the year was €1,650, up 7.8% on the same period in 2017.
However, there was a small drop of less than 1% recorded versus the third quarter of the year.
Cork had the second highest average rents, followed by Galway, Limerick and Waterford.
In the Greater Dublin area of Meath, Kildare and Wicklow, rental costs were 5% higher at the end of the final quarter of 2018 than they were at the end of the same period 12 months earlier.
While in the rest of the country, the cost of renting a home was up nearly 6%.
Responding to the latest data, the Minister for Housing, Eoghan Murphy, said it was encouraging to see rents falling for the first time in two years.
He said there is no doubt that rents remain too high in some places, but added that this is the first decrease since Rent Pressure Zones came into force.
However, the Simon Communities of Ireland said the figures highlight the difficulties faced by people relying on the private rental sector for secure and affordable accommodation.
It said that while it is encouraging that average rents fell compared to the previous quarter, they remain far too high nationwide.
It added that the continuing inaccessibility of the rental sector is both pushing people into homelessness and making it harder for those who are homeless to leave it behind.