There are 19 new locations designated as Rent Pressure Zones following a change in the criteria.
It means rent increases are limited to a maximum of 4% each year, with around two-thirds of renters now covered by RPZs.
The data shows that between the start of January and the end of March, the average rent stood at €1,169 per month.
The move comes as new figures from the Residential Tenancies Board show that nationally rents were over 8% higher during the first three months of the year, compared with the same time in 2018.
The figure represents an increase of €90 or 8.3% on the same period a year earlier.
When compared with the previous quarter, rents rose by 2.1%, reversing the fall recorded between the start of October and the end of December.
It was also the highest rate of annual price inflation in the rental market since the second quarter of 2016.
The RTB has said there was "continued growth in rental inflation and affordability issues in the sector".
The report shows the average rent for new tenancies is €1,245 per month, compared to €984 for renewed tenancies.
The highest average rent is in Dublin at €1,662, while Leitrim is the county with the lowest average rent at €537.
Meanwhile, rents in Waterford city recorded the biggest annual increase between January and March, up by 13.7% to €826, compared to the same time the previous year.
The Residential Tenancies Board has also been given new powers to address improper conduct by landlords under the Residential Tenancies Act.
The RTB can now directly investigate and sanction in cases where there are specific breaches of Residential Tenancy Law in relation to Rent Pressure Zones, false or misleading notices of termination and the non-registration of a tenancy.
Anyone found in breach of the legislation could face sanctions that range from a warning to a fine of up to €15,000.
The new legislation also requires that all notices of termination where the tenancy has been ended are required to be notified and copied to the RTB within 28 days of the tenancy ending.
Director of the Residential Tenancies Board Rosalind Carroll welcomed the new powers for her organisation, saying it finally gives the RTB "a regulatory toolkit" to deal with some cases that they have not been able to deal with until now.
She told RTÉ's Morning Ireland that the RTB will have strong investigatory powers and its objective is to achieve compliance.
"We have a full range of powers under this where we can ask people to provide us with their bank statements, tenancy agreements," she said.
"We can even go in and search a property if we need to. So quite extensive powers that, I think, will give us what we need to get into that regulatory area."
Ms Carroll urged tenants who think there has been a breach to contact the RTB.
The Chief Executive of Threshold also welcomed the move, saying it gives reassurance to renters.
Speaking on RTÉ's Today with Sean O’Rourke, John-Mark McCafferty added that new powers given to the RTB meant that the rent pressure zone area of legislation will now have more teeth.
Mr McCafferty said a delicate balance between protection for landlords and protection for tenants needed to be struck.
However, speaking on the same programme, a spokesperson for the Irish Property Owners Association described the extension of rent property zones as "a mistake".
Margaret McCormack said that rent control in Ireland was a very blunt instrument that did not take a number of factors into account, including the level of indebtedness of the landlord or the cost of provision of accommodation.
She said the problem with the homelessness crisis was supply, adding that the private rented sector was not responsible for the social housing issue.
During Leaders' Questions in the Dáil, Labour leader Brendan Howlin said the Government policy of increasing Rent Pressure Zones is not working as the 4% cap on rent increases has given a signal to landlords to increase rents by 4% each year.
Mr Howlin said that wages are not growing at 4% and affordability should be the benchmark on what is affordable to people.
Minister Richard Bruton disagreed and said the record of the Rent Pressure Zones is that they have helped to contain the growth of rents.
He said the key to the problem is increasing supply.
He added that there is evidence that year on year social homes, supported homes and private homes are increasing year on year.
Mr Howlin agreed that supply is the issue but he said that we cannot allow people be thrown out of their homes because of increases in rents.
He said that there needs to be an interim proposal of having a cap on rents and link it to wages across the State.
Meanwhile Solidarity/People Before Profit TD Richard Boyd Barrett has said that the
extension of Rent Pressure Zones to a number of new areas indicates that the housing and rental crisis is spreading around the country.
Speaking on RTÉ's Drivetime, Richard Boyd Barrett said the RPZ measures do little to deal with the unaffordability of housing.
Mr Boyd Barrett said that a 4% increase in rent, as allowed under the RPZ legislation, makes a property 4% more unaffordable.
He also said that the continual increase in rents means that people are left in "limbo" as they cannot get affordable housing, rents are through the roof and those rents are now going up by 4% a year.