The Anti-Austerity Alliance has said that, should they be part of the next government, they would compensate households who have already paid their water charges.
Socialist Party TD Joe Higgins said: "seeing as people have already paid for water through their taxes, the appropriate mode of compensation would be tax relief".
It came to light earlier this week that 57% of households had not paid their first water bill.
Sinn Féin are currently examining the question of repayments.
"This is a complicated issue", Senator Trevor Ó Clochartaigh said, "there are legal implications involved in repaying people who have already paid. These issues have arisen before with regards to other payments in the past. We are currently looking at the issue though."
Earlier, the AAA said it wants all organisations opposed to water charges to boycott bills.
At a press conference in Dublin, TD Ruth Coppinger said Sinn Féin and trade unions should come out and support their call.
Paul Murphy also called on landlords not to act as what he called "enforcers" for Irish Water.
The TD said the tenant is liable for the bill and the landlord should not try to enforce the charge.
A protest against water charges, organised by Right to Water, will take place in Dublin on 29 August.
