The National Payments Plan has said it will recommend to the Government that a trial in Wexford in which one and two cent coins were taken out of circulation be rolled out nationally.
One and two cent coins are minted more than other coins, but they go out of circulation quickly as people stockpile them.
The coins also cost more to mint than they are worth.
The results of the rounding trial, which was run from 16 September to 17 November 2013, showed strong support for rounding from both consumers and retailers.
During the trial, retailers rounded cash transactions to the nearest five cent at the cash register, removing the need for one cent and two cent coins in change.
Five EU member states, including The Netherlands, Sweden, Finland, Denmark and Hungary, have already adopted a rounding policy.
Speaking on RTÉ's Morning Ireland, NPP Programme Manager Ronnie O'Toole said that prices in Wexford did not go up as a result of the initiative.
Mr O'Toole said that the NPP ran a "mystery shopping" survey, in which it went into a number of shops and bought a set number of items before and after the trial.
It found that there was no change in the price of the goods that they bought.