New figures from the Central Statistics Office show that the number of new cars licensed for the first time in May fell by 5.4% on the same time last year.
However, the number of used or imported cars licensed for the first time soared 40.9% to 7,732 as car buyers continued to cross the border to take advantage of the weakness in sterling.
The CSO said that a total of 9,581 new private cars were licensed last month, down from the figure of 10,125 the same month last year.
The total number of new goods vehicles sold last month was also lower - down 13.7% to 2,185 from 2,531.
For the first five months of the year, the CSO said that 83,761 new cars were licensed, down 10.3% on the same time last year.
But the number of used private cars licensed motored 49.6% higher for the same period, the CSO added.
Today's figures from the CSO show that the top five near car models licensed in May were the Nissan Qashqui, the Hyundai Tucson, the Skoda Octavia, the Renault Clio and the Ford Fiesta.
In the first five months of the year, 65.7% of new private cars were diesel.
Licensing differs from registration in that a vehicle is licensed when a valid motor tax disc is issued for the first time. Registration occurs when a vehicle gets its licence plate (or registration number) for the first time.
Meanwhile, the CSO has today launched an online application (Ireland's Top Motors) allowing people to view vehicle licensing data and rank their own car model for a particular month.
The new application also presents annual data on private cars, commercial vehicles, motor cycles and tractors in graphical form and will allow users to follow trends in fuel types, colours and top makes.