The Tánaiste says the special Oireachtas committee on water charges must decide if people who are paid bills are to be repaid.
The Government says the decision will have to be made within three months.
Last night, Finance Minister Michael Noonan suggested at the Fine Gael Parliamentary Party that there was now enough money in the exchequer to make refunds if that is what is decided.
He told a meeting of Fine Gael TDs and senators that exchequer returns for November would be €280m ahead of expectations.
It means the State would be able to afford refunds for the €144m paid in water charges last year - although Mr Noonan did not indicate whether he supported spending money for that purpose.
Frances Fitzgerald told the Dáil the committee must decide, but everyone must be treated fairly.
"People on this side of the house would not stand over a situation where people who did the right thing and paid their charges would be disadvantaged in any way by their decision to obey the law," she argued.
"We wouldn't stand over a situation where people who disobeyed the law benefit over those who obeyed," she added.
The special committee will submit a report to both Houses of the Oireachtas by the end of February 2017, or within three months of its first public meeting
It remains unclear if those who refused to pay before the charges were suspended will be prosecuted.
But Minister Leo Varadkar does not believe it should happen.
"It's going to be up to the committee to make recommendations as to what we do now - but certainly my own view is that they shouldn't be refunded.
"The €140m that was paid went to Irish Water and went into our water network, and that's where we need more investment - not less.
"And for those who didn't pay, it's an unpaid bill and an outstanding debt - just like an unpaid ESB bill or an unpaid management charge.
"And ultimately eventually, one way or another, people will end up having to pay that bill".
Stephen Donnelly, Independent TD for Wicklow and East Carlow, says people who paid their water charges have to be refunded.
He suggested we "cannot have a situation" where one person paid and their neighbour did not.
