The future of the Help-to-Buy scheme remains uncertain as ministers refused to say if they want to see it extended in its current form in the Budget.
It comes as more people on low and middle-incomes are being squeezed out of the housing market.
The grant of up to €20,000 for first-time buyers purchasing new-build homes is due to expire at the end of the year.
Finance Minister Paschal Donohoe will announce news on its future in the Budget.
Fianna Fáil - which has been highly critical of the Government's delivery of affordable housing - has called for the scheme to be extended for at least three more years, with the cap on the value of a property left at €500,000.
Housing minister Eoghan Murphy claimed it was "a bit rich" for Fianna Fáil to be "lecturing" anyone on housing due to its management of the sector before the economic crash.
But he would not say if he wants to see the Help-to-Buy scheme extended in its current terms. He said he was in negotiations with Mr Donohoe and "couldn't publicly comment on it at this point".
Culture Minister Josepha Madigan also declined to give her view, saying it was a matter for Mr Murphy to discuss with Mr Donohoe.
Mr Murphy is understood to be seeking the extension of the grant, while Taoiseach Leo Varadkar hinted that this would happen in July. He told the Dáil that the grant "will help many more people in the future".
However, there have been reports that Mr Donohoe is considering changes to the cap on the value of a property, which could hit first-time buyers in urban areas if it is lowered.
Mr Murphy and Ms Madigan were at the turning of the sod at a development of 50 'cost rental' homes at Stepaside, south Co Dublin. The scheme is aimed at people who do not qualify for social housing, but cannot afford spiralling rents.
Mr Murphy hopes it will be a model for similar developments around the country.
Meanwhile, house prices have risen so much that many buyers now need an income over €80,000 to get approved for a mortgage and a large proportion of first-time buyers now have joint incomes.
The findings from the latest edition of Banking and Payments Federation of Ireland 'Housing Market Monitor' come as house prices move closer to their Celtic Tiger peaks.
The surge in property prices is despite household income lagging behind. Typical first-time borrowers now have an income of €71,000, up 3pc on the figure for last year.
In Dublin, the median income of a first-time buyer is now €84,000, the highest level since the series began in 2012.
In Cork, Galway and Limerick, the median income is €68,000. Nationally, the numbers of new buyers with an income exceeding €80,000 has doubled in the past decade, and a half to a third of new buyers.
Separately, the Cabinet is today set to decide on extending the Abhaile advice service for people in mortgage arrears for another three years at a cost of just over €17m.
Justice Minster Charlie Flanagan and Social Protection Minister Regina Doherty are expected to bring a memo to Government outlining the plans for the service, which has provided advice to more than 12,000 households.