More than 153,000 motorists in the State now have penalty points on their driving licences, according to the latest figures from the Department of Transport.
The Minister for Transport said the points system was having a significant impact on driver behaviour but the number of deaths on the roads could not be tolerated.
Mr Brennan said he believed the penalties would continue to instill greater caution amongst drivers.
"The consequences of losing a licence becomes a reality for drivers who have incurred points," he said.
"And they think twice before committing further breaches which will put them closer to the 12-point threshold."
Some 153,312 drivers were issued with points up to the end of May. The majority of those who have points, a total of 146,498, received them for speeding. Over 6,000 motorists now have points for not wearing a seatbelt, while 215 were penalised for carrying a child as a front-seat passenger without a seatbelt. Just 56 motorists received penalty points for having no insurance, which carries five penalty points.
Mr Eddie Shaw, chairman of the National Safety Council said: "Many drivers in this country believe that it is acceptable to drive at a few miles per hour over the speed limit. This is a dangerous attitude as there is no such thing as safe speeding."
Additional reporting PA