Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin met this evening to discuss an extension to the Confidence and Supply arrangement.
Teams from the parties will now be appointed this week and will hold their first meeting next week.
The move comes after Mr Martin suggested both men should agree not to cause an election while the Brexit negotiations are at their peak.
His offer has been met with some scepticism by Fine Gael who fear they are being lured into a situation that would allow Fianna Fáil call an election early in the New Year, when the housing and health crises tend to be at their worst.
Earlier today Mr Martin told reporters that his proposal was "very reasonable".
He said Fianna Fáil will enter talks on a "review" of the confidence and supply deal, which has allowed for the passing of three budgets, in good faith.
He refused to be tied to a timeline for when the talks on a new deal should end.
Mr Varadkar has indicated a desire to conclude a new arrangement by early-November.
He wants the extension to run until summer 2020.