The latest Residential Tenancies Board rent index shows that, nationally, rents rose by just under 10% in the second quarter of this year, when compared to last year.
In Dublin, rents are now at a new high, 3.9% above the previous peak in 2007.
The Simon Communities in Ireland have said the figures show the market is not slowing down, despite rent stability measures introduced last year.
The RTB index shows that 25% of all properties rented in April, May and June this year in Dublin cost more than €1,300 a month.
RTB Director Rosalind Carroll said there is a continuing lack of supply and an increase in short-term lets has left fewer properties available for long-term leases.
Significant increases were also seen nationally, with rents up 9.9% in the second quarter this year.
Rents for houses nationally were up 9.3% from €850 to €929 per month - and apartments increased by 11.7%, up from €908 to €1,014 per month.
However, while rents outside the capital are increasing, they are still 11.2% off their peak levels.
Ms Carroll said the RTB now has a total of 323,271 tenancies registered, representing 172,121 landlords and 704,332 occupants.
Speaking on RTÉ's Morning Ireland, she said the return of migrants is another contributing factor to the shortage of supply, with "more people coming into the country, probably particularly into the cities.
"We obviously have continued under-supply and seasonal factors, short-term lets happening more and more and that's putting more pressure on the market."
Ms Carroll also stated that relationships between landlords and tenants are generally working well.
"We have a slight increase in the disputes but nothing significant.
"We had over 4,000 disputes last year, but that only represents 1% or 2% of all tenancies so that shows most relationships are working well between landlords and tenants."
She said the nature of disputes has somewhat changed with more issues such as rent arrears and over-holding - where people stay beyond their notice of termination - indicating that perhaps these people have nowhere to go.
The chairperson of the housing charity Threshold said many of its clients are subjected to rent increases as high as 30% and urgent action is needed to tackle what she termed a situation akin to a "runaway train" .
Speaking on RTÉ's Today with Sean O'Rourke, Dr Aideen Hayden said the rent freeze introduced last year has protected some people in existing leases and has helped somewhat.
However, she said there is "a window where the rent freeze will end" and said Threshold is disappointed that Government strategy did not introduce a model of rent certainty to link rents to an index such as the Consumer Price Index.
Director of the Residential Landlords Association Fintan McNamara said rent control is one reason for the rise in rents.
Speaking the same programme he said landlords know that when they rent a place now it is fixed for two years and they can make no changes.
"And any rent they get, 60% goes back to the State in taxes and charges."
He said the rent control which was brought in last year has had some benefit for those in situ.
"That is why 80% fewer properties are advertised for rent now than they would be in a normally functioning market. It is harder to get accommodation."
Mr McNamara said that when rents are rising you would expect that landlords would come in and expand their properties to benefit from this.
"In fact many are not expanding but downsizing and some are getting out of the business altogether," he said.