Leo Varadkar and Micheal Martin have agreed to exploratory talks between Fine Gael and Fianna Fail.
They spoke over the phone last night and Mr. Varadkar has said he has accepted an invitation for similar talks from the Green Party.
Fine Gael has already said it's intending to go into opposition and not form part of a programme for government.
Meanwhile, Mr. Varadkar has officially resigned as Taoiseach after no candidate was elected at the first meeting of the 33rd Dáil.
He says he will stay on with his government until a new one is formed: