A new rent index says the national standardised average rent has grown by 9.5% in the past year.
The Residential Tenancies Board (RTB) Rent Index for the third quarter of the year shows the average rent for new tenancies was €1,056 per month.
That is up from €965 one year earlier.
It says the rate of rental growth has increased in the quarter when compared to Q1 and Q2 this year.
In Dublin, the average rent was at €1,518, with the average for the greater Dublin area (Meath, Wicklow and Kildare) at €1,086.
Outside of the Greater Dublin Area, the average rent was €811.
the board has also launcheed an education and awareness campaign, calling for landlords and tenants to ensure rents being charged are in line with the law.
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The RTB Rent Index is based on data from all new tenancy agreements registered with the RTB.
In total 29,528 new tenancies were registered in Q3 - an increase of over 6,000 registrations since the last quarter.
In percentage terms, nationally rents grew 9.5% over the year to Q3.
Rents in were 7% above their previous peak recorded in 2007.
While rents began growing again in late 2012, the RTB says the acceleration in the pace of growth, beginning in early 2014, continued in the most recent quarter.
"This follows a moderate slowdown in the pace of growth in Q4 2016 and Q1 2017", it says.
Commenting on the new index, RTB director Rosalind Carroll said: "Strong demographic and economic growth matched with low levels of supply is continuing to put significant pressure on the private rental market and those trying to find a place to live.
"This is the third Rent Index report published since Rent Pressure Zones were introduced one year ago.
"Despite a moderate slowdown in the pace of growth in the first quarter of 2017, quarters two and three show that rents are continuing to trend upwards, with an increase in the pace of growth in quarter three.
"These findings reflect the unprecedented situation of continued low supply of properties and high demand in a volatile rental market.
"It is really important that tenants and landlords are aware of their obligations and this is why the RTB is launching a further awareness campaign today, which is aimed at creating greater awareness about rent pressure zones."
'Mandatory rent register'
The national housing charity, Threshold has reiterated its call for the introduction of a mandatory rent register and proper enforcement of legislation.
Its chief executive, John-Mark McCafferty, said: "A mandatory rent register would create clarity for tenants.
"A property price register already exists in this country so we see no reason why a similar resource could not be developed for renters, who continue to find themselves in a very vulnerable position.
"Without disclosing the names of either the tenants or the landlords, a register would provide clarity to renters as to the level of rent they should expect to pay for a particular property.
"Enforcement of rent pressure zone legislation is clearly a problem and we find it ridiculous that the RTB won’t put in place this very simple measure, which would be hugely beneficial."
Threshold chair, Dr Aideen Hayden, added: "It is shocking that homeless figures continue to rise in this country and the only long-term solution to this is the development of social housing on a large scale.
"Recent figures from the Dublin Regional Homeless Executive show that the private rented sector is a huge driver of homelessness in the region, with nearly half of the newly homeless from June to August 2017 coming from the private rented sector.
"It is in crisis and it is not going to improve until legislation is enforced and tenants are aware of their rights and landlords of their obligations".