Private sector rents rose almost 7 per cent since this time last year, according to figures compiled by the Economic and Social Research Institute.
The average monthly rent in the country is now €835, which is up from €781 in the same quarter of last year.
The Quarterly Rent Index shows that rents for houses are up 6.5 per cent with rents for apartments rising 7.8 per cent compared with the start of 2014.
The market outside Dublin has seen an annual rent increase of 5.3 per cent, while rents in the capital have seen significantly higher growth at 9.6 per cent.
House rents in Dublin have risen 9 per cent in past 12 months, and apartment rents are up 10.8 per cent.
This brings the monthly rent to €1,325 for a house and €1,205 for an apartment in the capital, compared with the average rent outside Dublin of €647.
Those renting in Dublin are now paying more than €100 extra every month, compared with an increase of just over €30 for renters outside the capital.
Despite the increases, private accommodation rents across the whole country at the start of this year were 16.9 per cent lower than their peak, which occurred at the end of 2007.
Almost 1 in 5 households in the country are renting their accommodation in the private sector, according to the last census in 2011.
The director of the Private Residential Tenancies Board, Anne Marie Caulfield, has said that "in a market with rising rents, it is important that both landlords and tenants know it is not permissible to charge more than the market rent, and that rents can only be increased once in a 12-month period".