The Dáil will vote next week on whether or not to support a rent freeze on existing and new tenancies.
Sinn Féin has moved a bill calling for rents to be immediately frozen for three years, with all new rental properties pegged at market rates in that area.
If passed, it means rents would be frozen at current levels until at least 2023.
The bill also calls for a review of whether tax reliefs could be given to renters.
In recent weeks Fianna Fáil has said it supports the idea of freezing rents - and the party will now decide whether the bill passes or fails in a vote next Thursday.
Introducing his party's bill, Sinn Féin TD Eoin Ó Broin told the Dáil: "There's a growing number of people - many of them young, but some of them at the later stage of their working life, and whose incomes are between €35,000 and €75,000 - who simply cannot afford to rent accommodation at reasonable rates in our cities and, increasingly, in our towns.
"Sinn Féin and other opposition parties have been calling for a rent freeze - a freeze on all rents for existing tenancies and new tenancies."
He added: "[We've also called] for a refundable tax credit to put a month's rent back in renters' pockets: because freezing rents at such high and unsustainable levels is in and of itself not enough... we need to reduce rents as well."
Deputy Ó Broin has called on Fianna Fáil to back the bill - suggesting Micheál Martin "has a chance to put his money where his mouth is and decide if his party is willing to support renters".
The bill is due to be moved during private members time next Tuesday.