Simon Coveney says the deal has been offered with Independent TDs
The Taoiseach Enda Kenny has formally offered Fianna Fáil leader Michael Martin a full partnership government.
The acting Agriculture Minister Simon Coveney says the partnership has been offered with Independent TDs.
He tweeted, calling the deal "a historic change and good for Ireland".
Taoiseach has formally offered Michael Martin a full partnership Govt with Independent TDs - a historic change and good for Ireland— Simon Coveney (@simoncoveney) April 6, 2016
In a statement, Fine Gael says both leaders "had a positive and constructive meeting".
It says they discussed the current political situation and options for the formation of "a stable and lasting government".
"The Taoiseach made a formal offer for the formation of a full partnership Government including Fine Gael, Independents and Fianna Fail - which would have the potential to provide a stable and lasting government".
"The Taoiseach and the Fianna Fail Leader have agreed to meet again tomorrow for further discussions", it adds.
The two leaders met today after they both failed in their efforts to be elected Taoiseach.
Mr Kenny was defeated by 80 votes to 51, while Mr Martin was defeated by 95 votes to 43.
Irish Times political correspondent Sarah Bardon says Mr Martin will take the proposal to the Fianna Fáil parliamentary party.