The chairman of the Dáil Transport Committee, Mr Eoin Ryan, proposed a special meeting to discuss the increase in road accident deaths in the State this year.
He made his request as the Irish Insurance Federation, AA Ireland and the National Safety Council, amongst other groups, expressed concern at the rise in deaths. So far, 99 people have been killed on the roads this year, an increase of 22 on the same period in 2003.
"The increase in the number of fatalities from traffic accidents after last year's dramatic fall is extremely disappointing and raises questions about the operation of the penalty points system," Mr Ryan said.
He said the recent court decision dismissing five speeding cases because those charged claimed not to have received notice of their alleged offences was "a worrying development".
Mr Ryan said he would propose at the committee's meeting tomorrow that it invite the Garda National Traffic Bureau, the National Road Safety Council, the Department of Justice and the Department of Transport to attend a special meeting to be held "at the earliest opportunity".
The Irish Insurance Federation (IIF) said enforcement of traffic laws is the key to improving road safety and cutting deaths on the roads.
IIF Corporate Affairs Manager Mr Niall Doyle said: "This reversal in the downward trend in road accident fatalities has been noticeable since last October.
"This is directly attributable to drivers reverting to old habits due to their perception that regardless of the transgressions they commit the likelihood of them being caught is minimal.
"Following the statement by the Minister for Justice last week that an independent traffic corps was no longer being considered, the IIF is seeking a meeting with Minister McDowell and Minister Brennan to discuss alternative plans for an autonomous road traffic corps within the Garda structure," Mr Doyle said.
AA Ireland managing director Mr Pat Kiely said: "We simply don't enforce our road traffic laws well enough.
"The AA has consistently put the view that we must have a dedicated Garda Traffic Corps. Despite near universal acceptance that this is necessary, it still hasn't happened."
Today's calls come as EU transport ministers were meeting in Dublin to sign a charter aimed at halving the number of road deaths in 15 member states each year from 40,000 to 20,000 in six years.