The acting minister says they will go to their rivals after talks with Independents
Acting Minister Paschal Donohoe says Fine Gael and Fianna Fáil will hold coalition talks "in the future".
It comes as dicussions between Fine Gael, the Green Party and 15 independent TDs took place yesterday.
The TDs were divided into so-called 'breakout groups' to talk about individual subject areas.
However, there is agreement within Government Buildings that the support of Fianna Fáil will be needed to ensure a government is stable.
Mr Donohoe says talks between the main rival parties are inevitable.
"We owe it to those who have an interest in putting together a stable government to see if a programme for government is possible", he told Newstalk Breakfast.
"I would anticipate at the conclusion of those discussions and at a point in the future, we would then engage with other like-minded parties - which would include Fianna Fáil".
But asked if his Fine Gael party had reached out to Fianna Fáil, he replied: "At this moment, no we haven't".
However, Mr Donohoe says the two parties will sit down eventually.
While Fianna Fáil's Timmy Dooley says their options are limited.
But he believes there will be no real movement until the Dáil meets again on April 6th.