Sinn Féin TD Pearse Doherty has accused insurers of exaggerating the number of fraudulent claims to justify the rising cost of premiums.
The CEOs of AXA, Allianz and FBD which represent almost half of the Irish market were before an Oireachtas Committee today.
Despite the introduction of reform, the cost of premiums for consumers and businesses has not decreased.
Allianz chief Sean McGrath told the committee that the cost premiums will fall if more was done to tackle fraud.
He said he could not commit to how much premiums would fall by.
The competition and consumer protection committee have indicated that insurers are not to making public pronouncements about the future direction of pricing.
"We'd love to assist you and highlight what the savings could be but we believe that we're precluded from doing that.
"I will again give the guarantee that should claim costs come down, Allianz will reduce its pricing."